EXHIBIT 32

    CERTIFICATION PURSUANT TO SECTION 906 OF THE SARBANES-OXLEY ACT OF 2002



In connection with the filing of the Quarterly Report on Form 10-Q for the
quarter ended March 31, 2004 (the "Report") by Kirby Corporation (the
"Company"), each of the undersigned hereby certifies that:

        1.  The Report fully complies with the requirements of Section 13(a) or
            15(d) of the Securities Exchange Act of 1934, as amended; and

        2.  The information contained in the Report fairly presents, in all
            material respects, the financial condition and results of
            operations of the Company.


                                               /s/ JOSEPH H. PYNE
                                    ----------------------------------------
                                                 Joseph H. Pyne
                                      President and Chief Executive Officer



                                               /s/ NORMAN W. NOLEN
                                    ----------------------------------------
                                                 Norman W. Nolen
                                       Executive Vice President, Treasurer
                                           and Chief Financial Officer

Dated:  May 7, 2004