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, 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:  August 5, 2004