Exhibit 32.1

CERTIFICATION PURSUANT TO 18 U.S.C. SECTION 1350,

AS ADOPTED PURSUANT TO SECTION 906 OF

THE SARBANES-OXLEY ACT OF 2002

In connection with the Quarterly Report of Hornbeck Offshore Services, Inc., a Delaware corporation (the “Company”), on Form 10-Q for the period ending June 30, 2004, as filed with the Securities and Exchange Commission on the date hereof (the “Report”), I, Todd M. Hornbeck, President, Chief Executive Officer and Secretary of the Company, certify, pursuant to 18 U.S.C. Section 1350, as adopted pursuant to Section 906 of the Sarbanes-Oxley Act of 2002, that:

1. The Report fully complies with the requirements of Section 13(a) or 15(d) of the Securities Exchange Act of 1934; and

2. Information contained in the Report fairly presents, in all material respects, the financial condition and results of operations of the Company.

Dated: August 10, 2004

By: /s/ TODD M. HORNBECK

Todd M. Hornbeck

President, Chief Executive Officer and Secretary