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 this quarterly report of Possis Medical, Inc. on Form 10-Q
for the period ended October 31, 2006 as filed with the Securities and Exchange
Commission on the date hereof ("the Report"), I, Robert G. Dutcher, Chief
Executive Officer of Possis Medical, Inc., 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.   The information contained in this Report fairly presents, in all
          material respects, the financial condition and results of operations
          of Possis Medical, Inc.

Date: December 8, 2006      By:  /s/ Robert G. Dutcher
                             -----------------------------------------------
                             ROBERT G. DUTCHER
                             Chairman, President and Chief Executive Officer

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