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: June 14, 2004                                 /s/Robert G. Dutcher
                                                    ----------------------------
                                                    Robert G. Dutcher
                                                    Chairman, President and
                                                    Chief Executive Officer


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