<PAGE>   1


                UNITED STATES SECURITIES AND EXCHANGE COMMISSION

                             Washington, D.C. 20549

                                    Form 10-Q

            [X]         Quarterly report pursuant to Section 13 or 15(d) of the
                        Securities and Exchange Act of 1934

                        For the quarter ended March 31, 1998

            [ ]         Transition report pursuant to Section 13 or 15(d) of
                        the Securities and Exchange Act of 1934

Commission File Number  1-7615

                                Kirby Corporation
- --------------------------------------------------------------------------------
             (Exact name of registrant as specified in its charter)


              Nevada                                      74-1884980
   -------------------------------             --------------------------------
   (State or other jurisdiction of             (IRS Employer Identification No.)
   incorporation or organization)

             1775 St. James Place, Suite 200, Houston, TX      77056-3453
- --------------------------------------------------------------------------------
             (Address of principal executive offices)          (Zip Code)

                                 (713) 435-1000
- --------------------------------------------------------------------------------
              (Registrant's telephone number, including area code)

                                    No Change
- --------------------------------------------------------------------------------
              (Former name, former address and former fiscal year,
                          if changed since last report)

Indicate by check mark whether the registrant: (1) has filed all reports
required to be filed by Section 13 or 15(d) of the Securities Exchange Act of
1934 during the preceding 12 months (or for such shorter period that the
registrant was required to file such reports), and (2) has been subject to such
filing requirements for the past 90 days.

                            Yes   [X]         No   [ ]

The number of shares outstanding of the registrant's Common Stock, $.10 par
value per share, on May 6, 1998 was 21,393,764.



<PAGE>   2





                         PART 1 - FINANCIAL INFORMATION

                 KIRBY CORPORATION AND CONSOLIDATED SUBSIDIARIES

                            CONDENSED BALANCE SHEETS
                                   (Unaudited)

                                     ASSETS

<TABLE>
<CAPTION>

                                                                   March 31,   December 31,
                                                                     1998         1997
                                                                  ---------     ---------     
                                                                      ($ in thousands)
<S>                                                               <C>            <C>    
Current assets:
    Cash and cash equivalents                                     $  1,214         2,043
    Available-for-sale securities                                   22,324        21,773
    Receivables:
        Trade, net of allowance for doubtful accounts               60,198        70,137
        Insurance claims and other                                  13,184        14,458
    Inventories                                                     16,164        14,875
    Prepaid expenses and other current assets                        5,183         7,359
    Deferred income taxes                                            1,061         1,468
    Current assets of discontinued operations                         --           3,684
                                                                  --------      --------
            Total current assets                                   119,328       135,797
                                                                  --------      --------

Property and equipment, at cost                                    476,943       471,019
    Less accumulated depreciation                                  204,843       198,635
                                                                  --------      --------
                                                                   272,100       272,384
                                                                  --------      --------


Investments in affiliates:
    Insurance affiliate                                             45,779        45,320
    Marine affiliates                                               15,787        16,256
                                                                  --------      --------
                                                                    61,566        61,576
                                                                  --------      --------


Excess cost of consolidated subsidiaries, net of accumulated
    amortization                                                     6,495         6,652
Sundry                                                               4,418         4,562
Long-term assets of discontinued operations                           --          36,988
                                                                  --------      --------
                                                                  $463,907       517,959
                                                                  ========      ========
</TABLE>






           See accompanying notes to condensed financial statements.


                                       2

<PAGE>   3




                KIRBY CORPORATION AND CONSOLIDATED SUBSIDIARIES

                            CONDENSED BALANCE SHEETS
                                  (Unaudited)


                      LIABILITIES AND STOCKHOLDERS' EQUITY


<TABLE>
<CAPTION>

                                                                            March 31,     December 31,
                                                                              1998           1997
                                                                           ----------     ---------- 
                                                                                 ($ in thousands)
<S>                                                                         <C>            <C>    
Current liabilities:
    Current portion of long-term debt                                       $  5,333         5,333
    Income taxes payable                                                       6,880         4,319
    Accounts payable                                                          20,821        26,712
    Accrued liabilities                                                       52,932        54,193
    Deferred revenues                                                          2,462         5,046
                                                                            --------      --------
              Total current liabilities                                       88,428        95,603
                                                                            --------      --------

Long-term debt, less current portion                                         170,802       149,485
Deferred income taxes                                                         49,478        48,409
Other long-term liabilities                                                    6,241         6,193
                                                                            --------      --------
                                                                             226,521       204,087
                                                                            --------      --------

Contingencies and commitments                                                   --            --

Stockholders' equity:
    Preferred stock, $1.00 par value per share.  Authorized 20,000,000
        shares                                                                  --            --
    Common stock, $.10 par value per share. Authorized 60,000,000
        shares, issued 30,907,000 shares                                       3,091         3,091
    Additional paid-in capital                                               158,400       159,016
    Accumulated other comprehensive income                                       472           572
    Retained earnings                                                        141,985       136,945
                                                                            --------      --------
                                                                             303,948       299,624

    Less cost of 9,515,000 shares in treasury (6,619,000 at December
        31, 1997)                                                            154,990        81,355
                                                                            --------      --------
                                                                             148,958       218,269
                                                                            --------      --------
                                                                            $463,907       517,959
                                                                            ========      ========
</TABLE>





           See accompanying notes to condensed financial statements.


                                       3

<PAGE>   4


                 KIRBY CORPORATION AND CONSOLIDATED SUBSIDIARIES
                        CONDENSED STATEMENTS OF EARNINGS
                                   (Unaudited)


<TABLE>
<CAPTION>
                                                                           Three months ended
                                                                                March 31,
                                                                        -------------------------
                                                                           1998           1997
                                                                        ----------     ----------
                                                                        ($ in thousands, except per
                                                                              share amounts)
<S>                                                                      <C>              <C>   
 Revenues:
   Marine transportation                                                 $ 59,397         59,343
   Diesel repair                                                           22,858         20,545
   Investment income and other                                                457            393
   Gain (loss) on disposition of assets                                        36            (17)
                                                                         --------       --------

                                                                           82,748         80,264
                                                                         --------       --------
Costs and expenses:
   Costs of sales and operating expenses                                   54,712         54,787
   Selling, general and administrative                                      9,576         10,053
   Taxes, other than on income                                              1,981          1,748
   Depreciation and amortization                                            6,830          7,164
                                                                         --------       --------
                                                                           73,099         73,752
                                                                         --------       --------
        Operating income                                                    9,649          6,512
Equity in earnings of insurance affiliate                                     494            401
Equity in earnings of marine affiliates                                       716            863
Interest expense                                                           (2,767)        (3,374)
                                                                         --------       --------
        Earnings from continuing operations before taxes on income          8,092          4,402
Provision for taxes on income                                              (3,052)        (1,780)
                                                                         --------       --------
        Net earnings from continuing operations                             5,040          2,622

Earnings from discontinued operations, net of taxes on income                --            2,117
                                                                         --------       --------
        Net earnings                                                     $  5,040          4,739
                                                                         ========       ========

Net earnings per share of common stock:
    Basic:
        Continuing operations                                            $    .21            .11
        Discontinued operations                                              --              .08
                                                                         --------       --------
            Net earnings                                                 $    .21            .19
                                                                         ========       ========
    Diluted:
        Continuing operations                                            $    .21            .11
        Discontinued operations                                              --              .08
                                                                         --------       --------
            Net earnings                                                 $    .21            .19
                                                                         ========       ========
</TABLE>



           See accompanying notes to condensed financial statements.


                                       4

<PAGE>   5


                 KIRBY CORPORATION AND CONSOLIDATED SUBSIDIARIES
                       CONDENSED STATEMENTS OF CASH FLOWS
                                   (Unaudited)

<TABLE>
<CAPTION>
                                                                                       Three months ended March 31,
                                                                                      -----------------------------
                                                                                         1998              1997
                                                                                      ----------       ------------
                                                                                            ($ in thousands)
<S>                                                                                     <C>               <C>  
Cash flows from operating activities:
    Net earnings                                                                        $  5,040          4,739
    Adjustments to reconcile net earnings to net cash provided by continuing
    operations:
        Income from discontinued operations                                                 --           (2,117)
        Depreciation and amortization                                                      6,830          7,164
        Provision for deferred income taxes                                                2,288            880
        (Gain) loss on disposition of assets                                                 (36)            17
        Deferred scheduled maintenance costs                                               1,171          1,803
        Equity in earnings of insurance affiliate, net of redemption                        (494)         1,599
        Equity in earnings of marine affiliates, net of distributions and                
          contributions                                                                      469            176 
        Other                                                                                  8           --
        Increase in cash flows resulting from changes in operating working capital         5,019         (3,275)
                                                                                        --------       --------
             Net cash provided by operating activities of continuing operations           20,295         10,986
        Net cash provided by operating activities of discontinued operations                 276          4,802
                                                                                        --------       --------
             Net cash provided by operating activities                                    20,571         15,788
                                                                                        --------       --------
Cash flows from investing activities:
    Proceeds from sale and maturities of investments                                       1,034          1,935
    Purchase of investments                                                               (1,703)        (2,205)
    Capital expenditures                                                                  (6,199)        (6,246)
    Proceeds from disposition of assets                                                       77            750
    Proceeds from disposition of business                                                 38,600           --
    Investing activities of discontinued operations                                         (275)          (112)
                                                                                        --------       --------
            Net cash provided by (used in) investing activities                           31,534         (5,878)
                                                                                        --------       --------
Cash flows from financing activities:
    Borrowings (payments) on bank revolving credit agreements, net                        21,400        (15,100)
    Increase in long-term debt                                                              --           50,000
    Payments on long-term debt                                                               (83)       (34,000)
    Purchase of treasury stock                                                           (75,740)       (10,608)
    Proceeds from exercise of stock options                                                1,489            983
                                                                                        --------       --------
            Net cash used  in financing activities                                       (52,934)        (8,725)
                                                                                        --------       --------
            Increase (decrease) in cash and cash equivalents                                (829)         1,185

Cash and cash equivalents, beginning of year                                               2,043          1,544
                                                                                        --------       --------
Cash and cash equivalents, end of period                                                $  1,214          2,729
                                                                                        ========       ========
Supplemental disclosures of cash flow information: 
    Cash paid during the period:
        Interest                                                                        $    567          1,550
        Income taxes                                                                    $     33            294

</TABLE>



           See accompanying notes to condensed financial statements.



                                       5

<PAGE>   6


                 KIRBY CORPORATION AND CONSOLIDATED SUBSIDIARIES


                     NOTES TO CONDENSED FINANCIAL STATEMENTS


         In the opinion of management, the accompanying unaudited condensed
financial statements of Kirby Corporation and consolidated subsidiaries (the
"Company") contain all adjustments (consisting of only normal recurring
accruals) necessary to present fairly the financial position as of March 31,
1998 and December 31, 1997, and the results of operations for the three months
ended March 31, 1998 and 1997.

(1)      BASIS FOR PREPARATION OF THE CONDENSED FINANCIAL STATEMENTS

         The condensed financial statements included herein have been prepared
by the Company, without audit, pursuant to the rules and regulations of the
Securities and Exchange Commission. Although the Company believes that the
disclosures are adequate to make the information presented not misleading,
certain information and footnote disclosures, including significant accounting
policies normally included in annual financial statements, have been condensed
or omitted pursuant to such rules and regulations. It is suggested that these
condensed financial statements be read in conjunction with the Company's latest
Annual Report on Form 10-K.

(2)      ADOPTION OF ACCOUNTING STANDARDS

         Effective January 1, 1998, the Company adopted Statement of Financial
Accounting Standards ("SFAS") No. 130, "Reporting Comprehensive Income," which
establishes standards for reporting and display of comprehensive income and its
components in a full set of financial statements. Comprehensive income includes
all changes in a company's equity, including, among other things, foreign
currency translation adjustments, notes receivable from employee stock ownership
plans, deferred gains (losses) on hedging activities, and unrealized gains
(losses) on marketable securities classified as available-for-sale. The
Company's total comprehensive earnings for the three months ended March 31, 1998
and 1997 were as follows (in thousands):


<TABLE>
<CAPTION>
                                                Three months ended
                                                     March 31,
                                               ----------------------   
                                                1998           1997
                                               -------       --------
<S>                                            <C>             <C>  
Net earnings from continuing operations        $ 5,040         2,622
Net earnings from discontinued operations         --           2,117
                                               -------       -------
    Net earnings                                 5,040         4,739
Unrealized loss on marketable securities          (100)         (819)
                                               -------       -------
    Total comprehensive earnings               $ 4,940         3,920
                                               =======       =======
</TABLE>



         SFAS No. 131, "Disclosures about Segments of an Enterprise and Related
Information" ("SFAS No. 131"), issued in June 1997, establishes standards for
reporting information about operating segments in annual financial statements
and requires that enterprises report selected information about operating
segments in interim reports issued to shareholders. SFAS No. 131 will be adopted
by the Company in 1998. The adoption of SFAS No. 131 is not expected to have a
material impact on the Company's financial condition or results of operations.



                                       6

<PAGE>   7


                 KIRBY CORPORATION AND CONSOLIDATED SUBSIDIARIES

              NOTES TO CONDENSED FINANCIAL STATEMENTS - (Continued)


(3)      DISCONTINUED OPERATIONS

         On March 16, 1998, the Company announced the completion of the sale of
its U.S. flag product tanker and harbor service operations for $38,600,000 in
cash. Under the terms of a purchase agreement dated January 28, 1998, Kirby sold
two tankers and its harbor service operations to Hvide Marine Incorporated and
five tankers were sold to August Trading Company, Inc.

         The offshore tanker and harbor service operations' financial results
were accounted for as discontinued operations as of December 31, 1997, and
previously reported financial statements were restated to reflect the
discontinuation of the operations. The Company recorded an estimated net loss of
$3,966,000 as of December 31, 1997 from the sale of the tanker and harbor
service operations, and such results included a provision for operations during
the phase-out period, January 1, 1998 through the date of sale.

(4)      TAXES ON INCOME

         Earnings from continuing operations before taxes on income and details
of the provision for taxes on income from continuing operations for United
States and Puerto Rico operations for the three months ended March 31, 1998 and
1997 were as follows (in thousands):


<TABLE>
<CAPTION>


                                      Three months ended
                                           March 31,
                                     --------------------
                                       1998        1997
                                     --------    --------
<S>                                   <C>          <C>  
Earnings before taxes on income:
    United States                     $7,598       4,001
    Puerto Rico                          494         401
                                      ------      ------
                                      $8,092       4,402
                                      ======      ======
Provision for taxes on income:
     United States:
         Current                      $  505         536
         Deferred                      2,288         865
         State and local                 259         179
                                      ------      ------
                                       3,052       1,580

     Puerto Rico - Current              --           200
                                      ------      ------
                                      $3,052       1,780
                                      ======      ======
</TABLE>




                                       7

<PAGE>   8



                 KIRBY CORPORATION AND CONSOLIDATED SUBSIDIARIES

              NOTES TO CONDENSED FINANCIAL STATEMENTS - (Continued)



(4)      TAXES ON INCOME, Continued

         Earnings from discontinued operations before taxes on income and
details of the provision for taxes on income from United States discontinued
operations for the three months ended March 31, 1997 were as follows (in
thousands):



<TABLE>
<CAPTION>
                                                          Three months 
                                                              ended
                                                          March 31, 1997
                                                         ---------------
<S>                                                          <C>    
          Earnings before taxes on income:                   $ 3,261
                                                             =======
          Provision (credit) for taxes on income:
             United States:
               Current                                       $ 1,191
               Deferred                                          (38)
               State and local                                    (9)
                                                             -------
                                                             $ 1,144
                                                             =======
</TABLE>






                                       8

<PAGE>   9

                 KIRBY CORPORATION AND CONSOLIDATED SUBSIDIARIES

 
                    Management's Discussion and Analysis of
                  Financial Condition and Results of Operations



           Statements contained in this Form 10-Q that are not historical facts,
including, but not limited to, any projections contained herein, are
forward-looking statements and involve a number of risks and uncertainties. Such
statements can be identified by the use of forward-looking terminology such as
"may," "will," "expect," "anticipate," "estimate," or "continue" or the negative
thereof or other variations thereon or comparable terminology. The actual
results of the future events described in such forward-looking statements in
this Form 10-Q could differ materially from those stated in such forward-looking
statements. Among the factors that could cause actual results to differ
materially are: adverse economic conditions, industry competition and other
competitive factors, adverse weather conditions such as high water, low water,
fog and ice, marine accidents, construction of new equipment by competitors,
including construction with government assisted financing, government and
environmental laws and regulations, and the timing, magnitude and number of
acquisitions made by the Company.

           In March 1998, the Company completed the sale of its offshore tanker
and harbor service operations. In accordance with a definitive purchase
agreement dated January 28, 1998, the Company sold two tankers and its harbor
service operation to Hvide Marine Incorporated and five tankers to August
Trading Company, Inc., for a combined purchase price of $38,600,000 in cash. The
offshore tanker and harbor service operations' financial results have been
accounted for as discontinued operations as of December 31, 1997, and previously
reported financial statements have been restated to reflect the discontinuation
of the operations. Such financial results as of December 31, 1997 included a
provision for operations during the phase-out period, January 1, 1998 through
the date of sale.

           The Company is a provider of marine transportation services,
operating a fleet of 532 inland tank barges and 127 inland towing vessels,
transporting industrial chemicals and petrochemicals, refined petroleum products
and agricultural chemicals along the United States inland waterways. The
Company's marine transportation operation also includes a United States
coastwise barge operation, with two liquid and one dry bulk barge and tug units.
The Company also serves as managing partner of a 35% owned offshore marine
partnership, consisting of four dry bulk barge and tug units, and as managing
partner of a 50% owned offshore marine partnership, consisting of one dry bulk
barge and tug unit. The partnerships are accounted for under the equity method
of accounting.

           The Company is engaged through its diesel repair segment in the
overhaul and servicing of large medium-speed diesel engines employed in marine,
power generation and rail applications. The Company also has a 45% voting common
stock investment in Universal Insurance Company ("Universal"), accounted for
under the equity method of accounting.

RESULTS OF  CONTINUING OPERATIONS

           The Company reported net earnings from continuing operations of
$5,040,000, or $.21 per share, on revenues of $82,748,000 for the 1998 first
quarter, compared with net earnings from continuing operations of $2,622,000, or
$.11 per share, on revenues of $80,264,000 for the 1997 first quarter. For
comparative purposes, net earnings for the 1997 first quarter were $4,739,000,
or $.19 per share, including net earnings from discontinued operations of
$2,117,000, or $.08 per share, on revenues of $18,651,000. For purposes of this

Management's Discussion, all earnings per share amounts presented are "Diluted
Earnings Per Share."


                                       9

<PAGE>   10

                 KIRBY CORPORATION AND CONSOLIDATED SUBSIDIARIES

                     Management's Discussion and Analysis of
                  Financial Condition and Results of Operations


           The following table sets forth the Company's revenues from continuing
operations and percentage of such revenues for the three months ended March 31,
1998 compared with the three months ended March 31, 1997 (dollars in thousands):


<TABLE>
<CAPTION>
                                     Three months ended March 31,
                           -------------------------------------------------
                                   1998                        1997                Increase (decrease)
                           ---------------------      ----------------------      ----------------------
                            Amounts          %         Amounts           %         Amounts           %
                           --------        -----      ---------        -----      ---------        -----
<S>                        <C>               <C>       <C>               <C>       <C>               <C>
Revenues:
Marine transportation      $59,397            72%      $59,343            74%      $    54            --%
Diesel repair               22,858            28        20,545            26         2,313            11
Other income                   493            --           376            --           117            31
                           -------       -------       -------       -------       -------       -------

                           $82,748           100%      $80,264           100%      $ 2,484             3%
                           =======       =======       =======       =======       =======       =======
</TABLE>



           Revenues from the marine transportation segment reflected a
relatively flat 1998 first quarter compared with the first quarter of 1997.
However, the 1997 first quarter included transportation revenues of $2,478,000
from AFRAM Carriers, Inc. ("AFRAM"), the Company's U.S. flag offshore break-bulk
freighter subsidiary, which ceased operations in September and October 1997 with
the scrappage of the subsidiary's last two freighters.

           The Company's 1997 first quarter was also negatively impacted by high
water and flooding conditions which existed for the majority of the quarter on
the upper Mississippi River and the Ohio River. The flooding resulted in river
closures in selected areas for numerous days and mandated regulatory operating
restrictions. During the month of March 1997, the lower Mississippi River, the
Company's principal area of operations, experienced high water not seen in such
severity since 1983. The Company estimated its first quarter 1997 revenue loss
at $2,600,000 from the impact of the flooding. For the 1998 first quarter,
flooding conditions were relatively modest.

           During the 1998 first quarter, chemical and petrochemical volumes
were positive. Refined product volumes were soft, primarily due to seasonality,
and liquid fertilizer volumes were also soft, partially due to seasonality and
partially to high inventory levels, which delayed the spring filling of storage
facilities. Spot market rates continue to reflect a modest increase quarter to
quarter and contracts renewed during the 1998 first quarter were generally
renewed at higher rates.

           The diesel repair segment's revenues for the 1998 first quarter
reflected an 11% improvement compared with the 1997 first quarter. Business was
positive all across the diesel repair segment spectrum. The Gulf Coast market
remained strong due to the continued enhanced drilling activities and related
oil service activities in the Gulf of Mexico. The Midwest market was enhanced
with activities from Great Lakes customers and engine repairs for inland river
customers. The East Coast market benefited from large engine rebuilds currently
in progress, while the West Coast market improved due to enhanced relationships
with non-fishing industry customers. The diesel repair segment's 1997 first
quarter was negatively impacted by the flooding on the Mississippi River System,
as the Midwest inland towing companies deferred engine maintenance and
overhauls.


                                       10

<PAGE>   11


                 KIRBY CORPORATION AND CONSOLIDATED SUBSIDIARIES

                     Management's Discussion and Analysis of
                  Financial Condition and Results of Operations


           The following table sets forth the costs and expenses and percentage
of each for the three months ended March 31, 1998 compared with the three months
ended March 31, 1997 (dollars in thousands):


<TABLE>
<CAPTION>
                                                     Three months ended March 31,
                                           ---------------------------------------------------
                                                       1998                     1997                   Increase (decrease)
                                           -----------------------      ----------------------       -----------------------
                                             Amounts           %         Amounts           %          Amounts            %
                                           ----------        -----      ---------        -----       ---------         -----
<S>                                          <C>               <C>       <C>               <C>        <C>                <C> 
Costs and expenses:
Costs of sales and operating expenses        $54,712            75%      $54,787            74%       $   (75)            --%
Selling, general and administrative            9,576            13        10,053            14           (477)            (5)
Taxes, other than on income                    1,981             3         1,748             2            233             13

Depreciation and amortization                  6,830             9         7,164            10           (334)            (5)
                                             -------       -------       -------       -------        -------        -------
                                             $73,099           100%      $73,752           100%       $  (653)            (1)%
                                             =======       =======       =======       =======        =======        =======
</TABLE>




           Costs of sales and operating expenses for the 1998 first quarter
remained relatively constant compared with the first quarter of 1997. The prior
year first quarter included costs and expenses associated with the revenues
generated by AFRAM, whose vessels were scrapped in September and October 1997,
and higher costs and expenses associated with the flooding on the Mississippi
River. The 1998 first quarter reflected higher expenses for the diesel repair
segment associated with the 11% improvement in revenues.

           Selling, general and administrative expenses decreased 5% in the 1998
first quarter compared with the first quarter of 1997. The decrease reflects
savings in administrative expenses in the Company's diesel repair segment due to
reorganization efforts and the elimination of unprofitable business lines. To a
lesser degree, the decrease reflects the savings from the marine transportation
segment's costs reduction program implemented in late 1996 and is ongoing. The
program was designed to reduce administrative costs and improve operating
efficiencies.

           The 13% increase in taxes, other than on income was primarily
attributable to higher waterway use tax on inland operations based on ton miles
moved and higher property taxes on marine vessels.







                                       11

<PAGE>   12


                 KIRBY CORPORATION AND CONSOLIDATED SUBSIDIARIES

                     Management's Discussion and Analysis of
                  Financial Condition and Results of Operations


           The following table sets forth the operating income and operating
margins by segment for the three months ended March 31, 1998 compared with the
three months ended March 31, 1997 (dollars in thousands):


<TABLE>
<CAPTION>
                                   Three months ended March 31,
                       --------------------------------------------------
                                  1998                       1997            Increase (decrease)
                       --------------------------- ----------------------   --------------------
                        Operating                   Operating
                         income        Operating     income     Operating
                         (loss)          margin      (loss)       margin     Amounts         %
                       ----------      ----------  ---------    ---------   ----------    ------
<S>                     <C>             <C>        <C>            <C>       <C>             <C>
Marine transportation   $  8,144        13.7%      $  5,717       9.6%      $ 2,427         42%
Diesel repair              2,173         9.5%         1,547       7.5%          626         40
Corporate                 (1,161)                    (1,128)                    (33)        (3)
                        --------                   --------                 -------      -----
                        $  9,156                   $  6,136                 $ 3,020         49%
                        ========                   ========                 =======      =====
</TABLE>



           The following table sets forth the equity in earnings of affiliates
and interest expense for the three months ended March 31, 1998 compared with the
three months ended March 31, 1997 (dollars in thousands):



<TABLE>
<CAPTION>
                                                 Three months ended March 31,   Increase (decrease)
                                                  -------------------------    --------------------
                                                     1998           1997        Amount         %
                                                  ----------     ----------    ---------     ------
<S>                                               <C>            <C>           <C>            <C>  
Equity in earnings of insurance affiliate         $      494     $      401    $      93       23%
Equity in earnings of marine affiliates           $      716     $      863    $    (147)     (17)%
Interest expense                                  $   (2,767)    $   (3,374)   $    (607)     (18)%
</TABLE>



           The Company currently has a 45% voting common stock investment in
Universal. Accounted for under the equity method of accounting, the amount
recorded by the Company as equity in earnings for the Company's investment in
Universal is influenced to the extent that anticipated future redemptions by
Universal of its common stock exceeds the Company's investment in Universal's
stock. The Company also has a 100% investment in Universal's nonvoting preferred
stock. Because the preferred stock controls a separate portfolio of U.S.
Treasury Securities, the Company accounts for this preferred stock under SFAS
115. Therefore, the interest earned, as well as the realized gains from the sale
of U.S. Treasury Securities collateralizing the preferred stock, are included as
part of equity in earnings of the insurance affiliate. For the 1998 and 1997
first quarters, the Company recorded $259,000 and $251,000, respectively, of
interest earned from its investment in U.S. Treasury Securities.

           Equity in earnings of marine affiliates reflected a 17% decrease for
the 1998 first quarter compared with the 1997 first quarter. The offshore marine
partnerships vessels were fully employed during each comparable quarter, with
the exception of one offshore barge and tug unit, which, during the 1998 first
quarter, was in the shipyard for 15 days and idle for 30 days of the quarter.



                                       12

<PAGE>   13

                 KIRBY CORPORATION AND CONSOLIDATED SUBSIDIARIES

                     Management's Discussion and Analysis of
                  Financial Condition and Results of Operations


           Interest expense reflected an 18% decrease for the 1998 first quarter
compared with the first quarter of 1997. During the 1998 first quarter, excess
cash flow from operations and $38,600,000 in cash proceeds from the sale of the
offshore tanker and harbor service operations were used to pay down the
Company's bank revolving line of credit. The Company also benefited from lower
interest rates on the bank revolving line of credit. The Company's interest
expense did increase in mid-March 1998, with the increase in the bank revolving
line of credit to finance the "Dutch Auction" self-tender offer discussed below.

FINANCIAL CONDITION, CAPITAL RESOURCES AND LIQUIDITY

BALANCE SHEET

           Total assets as of March 31, 1998 were $463,907,000, a decrease of
10% compared with $517,959,000 as of December 31, 1997. The following table sets
forth the significant components of the balance sheet as of March 31, 1998
compared with December 31, 1997 (dollars in thousands):


<TABLE>
<CAPTION>

                                                                                       Increase (decrease)
                                                     March 31,     December 31,    ----------------------------
                                                       1998           1997           Amount              %
                                                    ----------     ----------      ----------        ---------- 
<S>                                                 <C>            <C>             <C>                    <C>  
Assets:
   Current assets                                   $ 119,328      $ 135,797       $ (16,469)             (12)%

   Property and equipment, net                        272,100        272,384            (284)            --

   Investments in affiliates                           61,566         61,576             (10)            --

   Long-term assets of discontinued operations           --           36,988         (36,988)            (100)

   Other assets                                        10,913         11,214            (301)              (3)
                                                    ---------      ---------       ---------        ---------
                                                    $ 463,907      $ 517,959       $ (54,052)             (10)%
                                                    =========      =========       =========        =========

Liabilities and stockholders' equity:
   Current liabilities                              $  88,428      $  95,603       $  (7,175)              (8)%

   Long-term debt                                     170,802        149,485          21,317               14

   Deferred taxes                                      49,478         48,409           1,069                2

   Other long-term liabilities                          6,241          6,193              48                1

   Stockholders' equity                               148,958        218,269         (69,311)             (32)
                                                    ---------      ---------       ---------        ---------
                                                    $ 463,907      $ 517,959       $ (54,052)             (10)%
                                                    =========      =========       =========        =========
</TABLE>



           As of March 31, 1998, working capital decreased to $30,900,000, a 23%
decrease compared with $40,194,000 at December 31, 1997. The decrease was
primarily attributable to the sale of the discontinued tanker and harbor service
property and equipment in mid-March 1998. Trade accounts receivable decreased
14%, reflecting the sale of the offshore operations. Inventories increased 9%,
the result of higher inventory levels at the Company's diesel repair facilities
to service the overall improving market. Accounts payable decreased 22%,
primarily reflecting the discontinued operations sold in mid-March 1998.

           The available-for-sale securities of $22,324,000 at March 31, 1998
and $21,773,000 at December 31, 1997 were investments of Oceanic Insurance
Limited, the Company's wholly owned captive insurance subsidiary.



                                       13

<PAGE>   14



                 KIRBY CORPORATION AND CONSOLIDATED SUBSIDIARIES

                     Management's Discussion and Analysis of
                  Financial Condition and Results of Operations


           Long-term debt, less current portion, increased 14% to $170,802,000
at March 31, 1998 compared with $149,485,000 at December 31, 1997. The
significant increase reflects the borrowing to finance the Company's Dutch
Auction self-tender offer to purchase shares of common stock, more fully
described below, net of the $38,600,000 of cash received from the sale of the
offshore tanker and harbor service operations.

           Stockholders' equity as of March 31, 1998 decreased 32% during the
1998 first quarter, reflecting the Company's purchase of 3,066,922 shares of its
common stock at a total purchase price of $75,740,000 under the Dutch Auction
self-tender offer, more fully described below. As of March 31, 1998, the Company
had 9,515,000 shares of common stock in its treasury.

LONG-TERM FINANCING

           The Company has a $100,000,000 revolving credit agreement (the
"Credit Agreement") with Chase Bank of Texas, N.A., as agent bank. Effective
January 30, 1998, the Credit Agreement was amended to provide a one-time
allowance for the disposition of assets at the subsidiary level. The amendment
also modified the minimum net worth covenant and fixed charge calculation.
Proceeds under the Credit Agreement may be used for general corporate purposes,
the purchase of existing or new equipment, the purchase of the Company's common
stock, or for possible business acquisitions. As of March 31, 1998, $54,000,000
was outstanding under the Credit Agreement.

TREASURY STOCK PURCHASES

           On March 23, 1998, the Company purchased 3,066,922 shares of its
common stock under a Dutch Auction self-tender offer at a price of $24.50 per
share. The Company announced the self-tender offer on February 17, 1998,
expressing its intentions to purchase up to 3,000,000 shares of its common stock
at a purchase price ranging from $21.00 to $24.50 per share. The tender offer
expired on March 16, 1998.

           The Company elected to increase the size of the 3,000,000 share
tender offer and to accept all shares tendered at a price of $24.50 per share.
The 3,066,922 shares purchased represented approximately 12.6% of the Company's
common stock outstanding immediately prior to the offer. Funding of the tender
offer was from the Company's Credit Agreement.

           The Company, as of May 5, 1998, has 1,814,000 shares available under
its Board of Directors' 6,250,000 total open market stock repurchase
authorization. The Company has not purchased any shares to date during 1998
under its open market stock repurchase authorization. The Company is authorized
to purchase its common stock on the New York Stock Exchange and in privately
negotiated transactions. When purchasing its common stock in the open market,
the Company is subject to price, trading volume and other market considerations.
Shares purchased may be used for reissuance upon the exercise of stock options,
in future acquisitions for stock or for other appropriate corporate purposes.





                                       14

<PAGE>   15


                 KIRBY CORPORATION AND CONSOLIDATED SUBSIDIARIES

                     Management's Discussion and Analysis of
                  Financial Condition and Results of Operations


LIQUIDITY

           The Company generated net cash provided by operating activities of
continuing operations of $20,295,000 and $10,986,000 for the three months ended
March 31, 1998 and 1997, respectively, reflecting a $8,294,000 change in
operating working capital. The Company accounts for its ownership in Universal
and its ownership in its 35% and 50% owned marine partnerships under the equity
method of accounting. It recognizes cash flow from Universal only upon receipt
of an actual distribution or redemption and cash flow from the marine
partnerships upon the receipt or disbursement of cash from the partnerships.
During the 1997 first quarter, the Company received $2,000,000 from Universal.
For the 1998 and 1997 first quarters, the Company received cash from the marine
partnerships of $1,185,000 and $1,039,000, respectively.

           Funds generated are available for capital construction projects,
treasury stock repurchases, asset acquisitions, repayment of borrowings
associated with treasury stock acquisitions or asset acquisitions and for other
operating requirements. In addition to its net cash flow provided by operating
activities, the Company also has available as of May 5, 1998, $40,000,000 under
its revolving credit agreement and $121,000,000 available under its medium term
note program. The Company's scheduled principal payments during the next 12
months are $5,333,000.

           During the last three years, inflation has had a relatively minor
effect on the financial results of the Company. The marine transportation
segment has long-term contracts which generally contain cost escalation clauses
whereby certain costs, including fuel, can be passed through to its customers,
while the transportation assets acquired and accounted for using the purchase
method of accounting were adjusted to a fair market value and, therefore, the
cumulative long-term effect of inflation was reduced. The repair portion of the
diesel repair segment is based on prevailing current market rates. The Company
does not presently use financial derivatives, but uses a mix of floating and
fixed rate debt. The Company has no foreign exchange risks.

           The Company has no present plan to pay dividends on its common stock.

YEAR 2000

           Historically, most computer systems utilized software that processed
transactions using two digits to represent the year of the transaction (i.e. 97
represents the year 1997). This software needs to be modified to properly
process dates beyond December 31, 1999 (the "Year 2000 Issue"). In the first
quarter of 1998, the Company completed its assessment of the Year 2000 Issue and
determined that no additional significant modifications or replacements of its
software were required. The Company utilizes both internally and externally
supported software and relies upon certain vendor enhancements yet to be
implemented to effect the Year 2000 Issue compliance. The Company presently
believes that these modifications to existing software and conversions to new
software will mitigate the Year 2000 Issue for its software.

           There can be no guarantee that the systems of other companies, on
which the Company's systems rely, will be timely converted, or that a failure to
convert by another company, or a conversion that is incompatible with the
Company's systems, would not have a material adverse effect on the Company.



                                       15

<PAGE>   16


                 KIRBY CORPORATION AND CONSOLIDATED SUBSIDIARIES

                     Management's Discussion and Analysis of
                  Financial Condition and Results of Operations


CONTINGENCIES

           On April 3, 1998, an organization identified as Pilots Agree called
for a work stoppage by vessel captains and pilots against the inland towing
companies' operating vessels on the inland waterway system of the United States.
Pilots Agree, an organization claiming to represent vessel wheelhouse personnel,
is asking for a substantial increase in pay. The work stoppage has had a minimal
impact on the Company's inland transportation operations.

ACCOUNTING STANDARDS

         SFAS No. 131, "Disclosures about Segments of an Enterprise and Related
Information," issued in June 1997, establishes standards for reporting
information about operating segments in annual financial statements and requires
that enterprises report selected information about operating segments in interim
reports issued to shareholders. SFAS No. 131 will be adopted in 1998. The
adoption of SFAS No. 131 is not expected to have a material impact on the
Company's financial condition or results of operations.







                                       16

<PAGE>   17


                 KIRBY CORPORATION AND CONSOLIDATED SUBSIDIARIES

 
                          PART II - OTHER INFORMATION



Item 1.    Legal Proceedings

           For a detailed explanation of the material pending legal proceedings
           against the Company, please refer to the Form 10-K for the year ended
           December 31, 1997.


Item 4.    Results of Votes of Security Holders

(a)        The Registrant held its Annual Meeting of Stockholders on April 21, 
           1998.

(b)        Proxies for the meeting were solicited pursuant to Regulation 14;
           there was no solicitation in opposition to management's nominees for
           directors as listed in the Proxy Statement, and all such nominees
           were elected.

           Directors elected were George F. Clements, Jr., C. Sean Day, Bob G.
           Gower, William M. Lamont, Jr., George A. Peterkin, Jr., J. H. Pyne,
           Robert G. Stone, Jr., Thomas M. Taylor and J. Virgil Waggoner. No
           other directors previously in office continued as a director or
           continued in office after the meeting.


Item 6.    Exhibits and Reports on Form 8-K

(a)        Exhibits:

           11.0  Computation of Earnings per Common Share.

           27.0  Financial Data Schedule.

(b)        Reports on Form 8-K:

           The Company filed a report on Form 8-K dated March 25, 1998 reporting
           the sale of two offshore tankers, land, facilities and its harbor
           service operations to Hvide Marine Incorporated and five offshore
           tankers to Sabine Transportation Corporation (an Iowa Corporation)
           for an aggregate $38,600,000 in cash.


                                   SIGNATURES

         Pursuant to the requirements of the Securities and Exchange Act of
1934, the Registrant has duly caused this report to be signed on its behalf by
the undersigned thereunto duly authorized.

                                          KIRBY CORPORATION
                                          (Registrant)



                                          By:  /s/  G. STEPHEN HOLCOMB
                                               -------------------------------
                                               G. Stephen Holcomb
                                               Vice President and Controller

Dated:     May 6, 1998



                                       17

<PAGE>   18

                                 EXHIBIT INDEX




<TABLE>
<CAPTION>
      EXHIBIT
      NUMBER     DESCRIPTION
      -------    -----------
      <S>        <C>
       11.0      Computation of Earnings per Common Share.

       27.0      Financial Data Schedule.
</TABLE>








<PAGE>   1

                                                                    EXHIBIT 11.0



                 KIRBY CORPORATION AND CONSOLIDATED SUBSIDIARIES

                    COMPUTATION OF EARNINGS PER COMMON SHARE





<TABLE>
<CAPTION>
                                                              Three months ended
                                                                    March 31,
                                                           -------------------------
                                                               1998          1997
                                                           -----------    ----------
                                                           (in thousands, except per
                                                                 share amounts)
<S>                                                          <C>           <C>  
Net earnings from continuing operations                      $ 5,040        2,622
Net earnings from discontinued operations                       --          2,117

                                                             -------      -------
    Net earnings                                             $ 5,040        4,739
                                                             =======      =======

Basic earnings per share:
Weighted average number of common shares outstanding          24,051       24,604
                                                             =======      =======

Basic earnings per share from continuing operations          $   .21          .11
Basic earnings per share from discontinued operations           --            .08
                                                             -------      -------
    Basic earnings per share                                 $   .21          .19
                                                             =======      =======

Diluted earnings per share:
Weighted average number of common shares outstanding          24,051       24,604
Dilutive shares applicable to stock options                      296          209

                                                             -------      -------
    Shares applicable to diluted earnings                     24,347       24,813
                                                             =======      =======

Diluted earnings per share from continuing operations        $   .21          .11
Diluted earnings per share from discontinued operations         --            .08

                                                             -------      -------
    Diluted earnings per share                               $   .21          .19
                                                             =======      =======
</TABLE>











<TABLE> <S> <C>

<ARTICLE> 5
<LEGEND>
THIS SCHEDULE CONTAINS SUMMARY FINANCIAL INFORMATION EXTRACTED FORM CONDENSED
CONSOLIDATED BALANCE SHEETS AND STATEMENTS OF EARNINGS AND IS QUALIFIED IN ITS
ENTIRETY BY REFERENCE TO SUCH FINANCIAL STATEMENTS.
</LEGEND>
<MULTIPLIER> 1,000
       
<S>                             <C>
<PERIOD-TYPE>                   3-MOS
<FISCAL-YEAR-END>                          DEC-31-1998
<PERIOD-END>                               MAR-31-1998
<CASH>                                           1,214
<SECURITIES>                                    22,324
<RECEIVABLES>                                   74,370
<ALLOWANCES>                                       988
<INVENTORY>                                     16,164
<CURRENT-ASSETS>                               119,328
<PP&E>                                         476,943
<DEPRECIATION>                                 204,843
<TOTAL-ASSETS>                                 463,907
<CURRENT-LIABILITIES>                           88,428
<BONDS>                                        170,802
<PREFERRED-MANDATORY>                                0
<PREFERRED>                                          0
<COMMON>                                         3,091
<OTHER-SE>                                     145,867
<TOTAL-LIABILITY-AND-EQUITY>                   463,907
<SALES>                                         17,199
<TOTAL-REVENUES>                                82,748
<CGS>                                           12,570
<TOTAL-COSTS>                                   54,712
<OTHER-EXPENSES>                                18,387
<LOSS-PROVISION>                                    26
<INTEREST-EXPENSE>                               2,767
<INCOME-PRETAX>                                  8,092
<INCOME-TAX>                                     3,052
<INCOME-CONTINUING>                              5,040
<DISCONTINUED>                                       0
<EXTRAORDINARY>                                      0
<CHANGES>                                            0
<NET-INCOME>                                     5,040
<EPS-PRIMARY>                                      .21
<EPS-DILUTED>                                      .21
        

</TABLE>