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 quarterly  report on Form 10-Q of Possis Medical,
          Inc. (Possis Medical);

     2.   Based on my  knowledge,  this  quarterly  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 quarterly report;

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

     4.   Possis  Medical's other  certifying  officer 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 Possis
          Medical and we 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  Possis  Medical,  including  its  consolidated
                    subsidiaries,  is made  known to us by others  within  those
                    entities,  particularly  during  the  period  in which  this
                    quarterly report is being prepared;

               b.   Evaluated the  effectiveness of Possis Medical'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 Possis  Medical's
                    internal  control over  financial  reporting  that  occurred
                    during Possis  Medical's most recent fiscal quarter  (Possis
                    Medical's  fourth  fiscal  quarter  in the case of an annual
                    report)  that  has  materially  affected,  or is  reasonably
                    likely  to  materially  affect,  Possis  Medical's  internal
                    control over financial reporting; and

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


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               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
                    Possis Medical'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 Possis
                    Medical's internal control over financial reporting.








Date: March 4, 2005                                 /s/ Robert G. Dutcher
                                                    ----------------------------
                                                        Robert G. Dutcher
                                                        Chairman, President and
                                                        Chief Executive Officer


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