EXHIBIT 32

                CERTIFICATION PURSUANT TO 13 U.S.C. SECTION 1350
     (AS ADOPTED 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 September 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: November 8, 2004