<PAGE>
 
                      SECURITIES AND EXCHANGE COMMISSION
                            Washington, D.C. 20549


                                 SCHEDULE 13G
            Information Statement Pursuant to Rules 13d-1 and 13d-2

 
 
                               Kirby Corporation
                              -------------------
                               (Name of Issuer)



                   Common Stock, $.10 par value per share  
                   ----------------------------------------
                        (Title of Class of Securities)




                                   497266106
                                  -----------
                                (CUSIP Number)





     Check the following box if a fee is being paid with this statement  X . (A
                                                                        ---
     fee is not required only if the filing person: (1) has a previous statement
     on file reporting beneficial ownership of more than five percent of the
     class of securities described in item 1: and (2) has filed no amendment
     subsequent thereto reporting beneficial ownership of five percent or less
     of such class.) (See Rule 13d-7.)






                       (Continued on following pages)   

                       
                               Page 1 of 9 Pages

<PAGE>
 
- ------------
CUSIP NO.
 497266106
- ----------
- --------------------------------------------------------------------------------
1.   Name of Reporting Person
     S.S. or  I.R.S. Identification No. of  Above Person

     Goldman, Sachs & Co.

- --------------------------------------------------------------------------------
2.   Check the Appropriate Box if a Member of a Group

                                                   (a)___
                                                   (b)___
- --------------------------------------------------------------------------------
3.   SEC Use Only


- --------------------------------------------------------------------------------
4.   Citizenship or place of  Organization

             New York
- --------------------------------------------------------------------------------
Number of      5    Sole Voting Power
Shares         
Beneficially            0                                
Owned By       ---------------------------------- 
               6    Shared Voting Power
Each
Reporting               2,061,500                         
Person With    ---------------------------------- 
               7    Sole Dispositive Power

                       0                                  
               ----------------------------------
               8    Shared Dispositive Power

                        2,061,500                        
               ----------------------------------
9.  Aggregate Amount Beneficially Owned by Each Reporting Person

                                        2,061,500
- --------------------------------------------------------------------------------
10.  Check if the Aggregate Amount in Row (11) Excludes Certain Shares


- --------------------------------------------------------------------------------
11.  Percent of Class Representing by Amount in Row (11)

                                         7.3%
- --------------------------------------------------------------------------------
12.  Type of Reporting Person

                                         BD-PN-IA
- --------------------------------------------------------------------------------


                               Page 2 of 9 Pages

<PAGE>
 
- ------------
CUSIP NO.
 497266106
- -----------
- --------------------------------------------------------------------------------
1.   Name of Reporting Person
     S.S. or  I.R.S. Identification No. of  Above Person

     The Goldman Sachs Group, L.P.

- --------------------------------------------------------------------------------
2.   Check the Appropriate Box if a Member of a Group

                                                   (a)___
                                                   (b)___
- --------------------------------------------------------------------------------
3.   SEC Use Only


- --------------------------------------------------------------------------------
4.   Citizenship or place of  Organization

         Delaware
- --------------------------------------------------------------------------------
Number of      5    Sole Voting Power
Shares         
Beneficially            0                                
Owned By       ---------------------------------- 
               6    Shared Voting Power
Each
Reporting               2,061,500                         
Person With    ---------------------------------- 
               7    Sole Dispositive Power

                        0                                  
               ----------------------------------
               8    Shared Dispositive Power

                        2,061,500                        
               ----------------------------------
9.  Aggregate Amount Beneficially Owned by Each Reporting Person

                                   2,061,500
- --------------------------------------------------------------------------------
10.  Check if the Aggregate Amount in Row (11) Excludes Certain Shares


- --------------------------------------------------------------------------------
11.  Percent of Class Representing by Amount in Row (11)

                                  7.3%
- --------------------------------------------------------------------------------
12.  Type of Reporting Person

                            HC-PN
- --------------------------------------------------------------------------------


                               Page 3 of 9 Pages

<PAGE>
 
     Item 1(a).    Name of Issuer:
                    Kirby Corporation

     Item 1(b).    Address of Issuer's Principal Executive Offices:
                   1775 St. James, Suite 300, Houston, TX  77056
                    
     Item 2(a).    Name of Person Filing:
                   Goldman, Sachs & Co. and  The Goldman Sachs Group, L.P.
               
     Item 2(b).    Address of Principal Business Office, or, if None, Residence:
                   Goldman, Sachs & Co. and The Goldman Sachs Group, L.P.
                   85 Broad Street,  New York, N.Y.  10004
               
     Item 2(c).    Citizenship:
                   Goldman, Sachs & Co. - New York
                   The Goldman Sachs Group, L.P. - Delaware
                    
     Item 2(d).    Title and Class of Securities:
                   Common Stock, $.10 par value per share

     Item 2(e).    CUSIP Number:
                   497266106

     Item 3.       If this statement is filed pursuant to Rules 13d-1(b), or 
                   13d-2(b). check whether the person filing is a :

             (a).X Broker or dealer registered under Section 15 of the Act,
                          Goldman, Sachs & Co.

             (b).  Bank as defined in Section 3(a)(6) of the Act,

             (c).  Insurance Company as defined in Section 3(a)(19) of the Act,

             (d).  Investment Company registered under Section 8 of the
                   Investment Company Act,

             (e).X Investment Adviser registered under Section 203 of the
                   Investment Advisers Act of 1940,
                          Goldman, Sachs & Co.


                               Page 4 of 9 Pages

<PAGE>
 
             (f).  Employee Benefit Plan, Pension Fund which is subject to the
                   provisions of the Employee Retirement Income Security Act of
                   1974 or Endowment Fund; see 13d-1(b)(1)(ii)(F),

             (g).X Parent Holding Company, in accordance with Rule 13d-
                   1(b)(ii)(G); see Item 7,
                          The Goldman Sachs Group, L.P.

             (h).  Group, in accordance with Rule 13d-1(b)(ii)(H).


      Item 4.      Ownership.

             (a).  Amount beneficially owned:
                   See the responses(s) to Item 9 on the attached cover
                   pages(s).

             (b).  Percent of class:
                   See the response(s) to Item 11 on the attached cover
                   pages(s).

             (c).  Number of shares as to which such person has:

                   (i)    Sole power to vote or to direct the vote:
                                See the response(s) to Item 5 on the attached
                                cover page(s).

                   (ii)   Shared power to vote or direct the vote:
                                See the response(s) to Item 6 on the attached
                                cover page(s).

                   (iii)  Sole power to dispose or to direct the disposition of:
                                See the response(s) to Item 7 on the attached
                                cover page(s).

                   (iv)   Shared power to dispose or to direct the disposition
                          of:
                                See the response(s) to Item 8 on the attached
                                cover page(s).

       Item 5.     Ownership of Five Percent or Less of a Class.
                          Not Applicable

       Item 6.     Ownership of More than Five Percent on Behalf of Another
                   Person.
                          Not Applicable

       Item 7.     Identification and Classification of the Subsidiary Which
                   Acquired the Security Being Reported on by the Parent Holding
                   Company.
                          See Exhibit(2)

       Item 8.     Identification and Classification of Members of the Group.


                               Page 5 of 9 Pages

<PAGE>
 
                        Not Applicable

      Item 9.    Notice of Dissolution of Group.
                        Not Applicable

      Item 10.   Certification.

                 By signing below I certify that, to the best of my
                 knowledge and belief, the securities referred to
                 above were acquired in the ordinary course of
                 business and were not acquired for the purpose of
                 and do not have the effect of changing or
                 influencing the control of the issuer of such
                 securities and were not acquired in connection with
                 or as a participant in any transaction having such
                 purpose or effect.



                                   SIGNATURE

          After reasonable inquiry and to the best of my knowledge and
          belief, I certify that the information set forth in this statement is
          true, complete and correct.


Date:  February 10, 1995


                                         THE GOLDMAN SACHS GROUP, L.P.

                                         By:     /s/ David B. Ford
                                            ------------------------------------
                                         Name:   David B. Ford
                                         Title:  General Partner

                                         GOLDMAN, SACHS & CO.

                                         By:     /s/ David B. Ford
                                            --------------------------
                                         Name:   David B. Ford
                                         Title:  General Partner


                               Page 6 of 9 Pages

<PAGE>
 
                               INDEX TO EXHIBITS





Exhibit No.      Exhibit
- -----------      -------

    99.1         Joint Filing Agreement, dated February 10, 1995, between The
                 Goldman Sachs Group, L.P., and Goldman, Sachs & Co.

    99.2         Item 7 Information

                               Page 7 of 9 Pages





<PAGE>
 
                                                                   EXHIBIT 99.1



                            JOINT FILING AGREEMENT




     In accordance with Rule 13d-1(f) promulgated under the Securities Exchange
Act of 1934, the undersigned agree to the joint filing of a Statement on
Schedule 13G (including any and all amendments thereto) with respect to the
shares of Kirby Corporation, and further agree to the filing of this agreement
as an Exhibit thereto. In addition, each party to this Agreement expressly
authorizes each other party to this Agreement to file on its behalf any and all
amendments to such Statement on Schedule 13G.



Date: February 10, 1995


THE GOLDMAN SACHS GROUP, L.P.              GOLDMAN, SACHS & CO.


By:     /s/ David B. Ford                  By:     /s/ David B. Ford
   ---------------------------                -----------------------------
Name:   David B. Ford                      Name:   David B. Ford
Title:  General Partner                    Title:  General Partner

                               Page 8 of 9 Pages





<PAGE>
 
                                                                   EXHIBIT 99.2



                              ITEM 7 INFORMATION




     Goldman, Sachs & Co. is a broker or dealer registered under Section 15 of
the Act and an investment adviser registered under Section 203 of the Investment
Advisers Act of 1940.

                               Page 9 of 9 Pages