Exhibit 99.1

                Possis Medical Inc., Announces its Inclusion in
                      the New NASDAQ Global Select Market


    MINNEAPOLIS--(BUSINESS WIRE)--June 27, 2006--

  The Market with the Highest Initial Listing Standards in the World

    Possis Medical, Inc. (NASDAQ:POSS) today announced that it is
included in the new NASDAQ Global Select Market. The NASDAQ Global
Select Market has the highest initial listing standards of any
exchange in the world based on financial and liquidity requirements.
Prior to the change, Possis had been listed on the NASDAQ National
Market.
    Beginning July 3, NASDAQ-listed companies will be classified under
three listing tiers: NASDAQ Global Select Market, NASDAQ Global
Market, and NASDAQ Capital Market. NASDAQ also plans to launch indexes
based on these new tiers.
    "Possis Medical is an example of an industry leader that has
achieved superior listing standards, which clearly defines the essence
of the NASDAQ Global Select Market," said Bruce Aust, Executive Vice
President, Corporate Client Group. "NASDAQ is focused on leading a
race to the top in terms of listing qualifications. In recognizing
these companies, we are highlighting their achievement in meeting the
requirements to be included in the market with the highest listing
standards in the world."
    Said Robert G. Dutcher, CEO of Possis Medical, "We're pleased to
be included in NASDAQ's top-tier listing. We feel that this will be a
positive for both our institutional and retail investors."
    NASDAQ announced the new three-tier listing classification in
February 2006. All three market tiers will maintain rigorous listing
and corporate governance standards. For additional information about
the NASDAQ Global Select Market, please go to:
www.nasdaq.com/GlobalSelect.

    About NASDAQ

    NASDAQ is the largest U.S. electronic stock market. With
approximately 3,200 companies, it lists more companies and, on
average, trades more shares per day than any other U.S. market. It is
home to companies that are leaders across all areas of business
including technology, retail, communications, financial services,
transportation, media and biotechnology. NASDAQ is the primary market
for trading NASDAQ-listed stocks. For more information about NASDAQ,
visit www.nasdaq.com or the NASDAQ Newsroom at
http://www.nasdaq.com/newsroom/.

    About Possis Medical, Inc.

    Possis Medical, Inc., develops, manufactures and markets
pioneering medical devices for the large and growing cardiovascular
and vascular treatment markets. Its AngioJet(R) Rheolytic(TM)
Thrombectomy System is marketed internationally for blood clot removal
from native coronary arteries, leg arteries, coronary bypass grafts
and AV dialysis access grafts. For more information about Possis
endovascular products visit www.possis.com.


    CONTACT: Possis Medical, Inc.
             Jules L. Fisher, 763-450-8011
             Jules.Fisher@possis.com