EXHIBIT 31.1

         Certification of Chief Executive Officer, Pursuant to Section 302 of
         the Sarbanes-Oxley Act of 2002




I, Robert G. Dutcher, certify that:

1.       I have reviewed this annual report of Possis Medical, Inc.;

2.       Based on my knowledge, this report does not contain any untrue
         statement of a material fact or omit to state a material fact necessary
         to make the statements made, in light of the circumstances under which
         such statements were made, not misleading with respect to the period
         covered by this report;

3.       Based on my knowledge, the financial statements, and other financial
         information included in this report, fairly present in all material
         respects the financial condition, results of operations and cash flows
         of the registrant as of, and for, the periods presented in this report;

4.       The registrant's other certifying officer(s) and I are responsible for
         establishing and maintaining disclosure controls and procedures (as
         defined in Exchange Act Rules 13a-15(e) and 15d-15(e)) for the
         registrant and have:

         a.       Designed such disclosure controls and procedures, or caused
                  such disclosure controls and procedures to be designed under
                  our supervision, to ensure that material information relating
                  to the registrant, including its consolidated subsidiaries, is
                  made known to us by others within those entities, particularly
                  during the period in which this report is being prepared;

         b.       Evaluated the effectiveness of the registrant's disclosure
                  controls and procedures and presented in this report our
                  conclusions about the effectiveness of the disclosure controls
                  and procedures, as of the end of the period covered by this
                  report based on such evaluation; and

         c.       Disclosed in this report any change in the registrant's
                  internal control over financial reporting that occurred during
                  the registrant's most recent fiscal quarter (the registrant's
                  fourth fiscal quarter in the case of an annual report) that
                  has materially affected, or is reasonably likely to materially
                  affect, the registrant's internal control over financial
                  reporting; and



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5.       The registrant's other certifying officer(s) and I have disclosed,
         based on our most recent evaluation of internal control over financial
         reporting, to the registrant's auditors and the audit committee of the
         registrant's board of directors (or persons performing the equivalent
         functions):

         a.       All significant deficiencies and material weaknesses in the
                  design or operation of internal control over financial
                  reporting which are reasonably likely to adversely affect the
                  registrant's ability to record, process, summarize and report
                  financial information; and

         b.       Any fraud, whether or not material, that involves management
                  or other employees who have a significant role in the
                  registrant's internal control over financial reporting.








Date: October 12, 2004                   /s/  Robert G. Dutcher
                                         ----------------------------------
                                         Signature

                                         Robert G. Dutcher
                                         Chairman, President and
                                         \Chief Executive Officer




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