Exhibit 99.1

    Possis Medical, Inc., to Present at the Jefferies Healthcare Conference

     MINNEAPOLIS--(BUSINESS WIRE)--June 21, 2007--Possis Medical, Inc.
(NASDAQ:POSS), today announced that it is participating in the Jefferies
Healthcare Conference in New York City on Thursday, June 28, 2007. Robert
Dutcher, president and CEO, is scheduled to present a company overview and
discuss Possis' pioneering medical technologies to conference attendees at 9:40
a.m. ET.

     A live audio webcast of the presentation will be available at 9:40 a.m. ET
on Thursday, June 28, at www.possis.com under the "Investors" tab. A replay will
be available at the same address for 90 days.

     Possis Medical, Inc., develops, manufactures and markets pioneering medical
devices for the large and growing cardiovascular and vascular treatment markets.
The Company's AngioJet System is the world's leading mechanical thrombectomy
system with FDA approval to remove large and small thrombus from coronary
arteries, coronary bypass grafts, peripheral arteries and veins, A-V grafts and
native fistulas.


     CONTACT: Possis Medical, Inc.
              Jules L. Fisher, 763-450-8011
              Vice President, Finance and
              Chief Financial Officer
              Jules.Fisher@possis.com