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 Possis Medical, Inc. (the Company) on
Form 10-Q for the period ended October 31, 2004 as filed with the Securities and
Exchange Commission on the date hereof ("the Report"), I, Robert G. Dutcher,
Chief Executive Officer 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, as amended; and

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

Date: December 9, 2004                    /s/ Robert G. Dutcher
                                          --------------------------
                                              Robert G. Dutcher
                                              Chairman, President and
                                              Chief Executive Officer

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