EXHIBIT 32

Certification Pursuant to Section 18 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 Annual Report on Form 10-K for the year ended December 31, 2012 (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 of the Board and

Chief Executive Officer

/s/    DAVID W. GRZEBINSKI

David W. Grzebinski

Executive Vice President and

Chief Financial Officer

Dated: February 27, 2013