Exhibit 32

Certification Pursuant to Section 18 U.S.C. Section 1350

In connection with the filing of the Quarterly Report on Form 10-Q for the quarter ended September 30, 2010 (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

Chairman, President and

Chief Executive Officer

/s/ DAVID W. GRZEBINSKI    

David W. Grzebinski

Executive Vice President and

Chief Financial Officer

Dated: November 5, 2010