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 June 30, 2003 (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:  August 12, 2003