Exhibit 32.1

                       Certification Furnished Pursuant to
                  Section 906 of the Sarbanes-Oxley Act of 2002

In connection with the Quarterly Report on Form 10-Q of Unifab International,
Inc. (the "Company") for the period ended June 30, 2004, as filed with the
Securities and Exchange Commission on the date hereof (the "Report"), the
undersigned, who is the Principal Executive Officer of the Company, certifies
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
            Section 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 for the period covered by the Report.

                                            /s/ William A. Hines
                                            ------------------------------------
                                            Name:  William A. Hines.
                                            Title: Principal Executive Officer
                                            Date:  August 14, 2004

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