Exhibit 32.1

CERTIFICATION PURSUANT TO

SECTION 906 OF THE SARBANES-OXLEY ACT OF 2002

(18 U.S.C. SECTION 1350)

In connection with the Quarterly Report of Flow International Corporation, a Washington corporation (the “Company”), on Form 10-Q for the quarter ending October 31, 2004 as filed with the Securities and Exchange Commission (the “Report”), I, Stephen R. Light, Principal Executive Officer of the Company, certify, pursuant to § 906 of the Sarbanes-Oxley Act of 2002 (18 U.S.C. § 1350), that to my knowledge:

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

(2) The information contained in the Report fairly presents, in all material respects, the financial condition and result of operations of the Company.

/s/    STEPHEN R. LIGHT

Stephen R. Light

Principal Executive Officer

January 10, 2005

CERTIFICATION PURSUANT TO

SECTION 906 OF THE SARBANES-OXLEY ACT OF 2002

(18 U.S.C. SECTION 1350)

In connection with the Quarterly Report of Flow International Corporation, a Washington corporation (the “Company”), on Form 10-Q for the quarter ending October 31, 2004 as filed with the Securities and Exchange Commission (the “Report”), I, Stephen D. Reichenbach, Principal Financial Officer of the Company, certify, pursuant to § 906 of the Sarbanes-Oxley Act of 2002 (18 U.S.C. § 1350), that to my knowledge:

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

(2) The information contained in the Report fairly presents, in all material respects, the financial condition and result of operations of the Company.

/s/    STEPHEN D. REICHENBACH

Stephen D. Reichenbach

Principal Financial Officer

January 10, 2005