EXHIBIT 99.1


Possis Medical, Inc., to Present at the SunTrust Robinson Humphrey Conference

    MINNEAPOLIS--(BUSINESS WIRE)--April 5, 2007--Possis Medical, Inc.
(NASDAQ:POSS), today announced that it is participating in the
SunTrust Robinson Humphrey 36th Annual Institutional Conference to be
held April 10 and 11 at the Ritz-Carlton Buckhead in Atlanta, Georgia.
Robert Dutcher, chairman, president and CEO, is scheduled to present a
company overview and discuss Possis' pioneering medical technologies
to conference attendees at 3:15 p.m. ET on April 10.

    A live Webcast of the presentation will be available just prior to
the presentation and will be available for online demand within 24
hours 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(R) 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