A vascular prosthesis (10) comprises pericardial, fascial, or other tissue (12) formed over a tubular support frame. A first exemplary tubular support frame comprises an inner helical member (16) and an outer helical member (14), where the tissue is rolled and captured therebetween. A second exemplary tubular support frame (60, 62) comprises a plurality of ring elements (64, 72) which are located alternately on the outside and on the inside of the rolled tissue. Other exemplary frames employ fasteners (84, 98) for penetrating the rolled tissue and attaching tissue to frame elements. The tissue is preferably obtained from the patient who is to receive the vascular prosthesis, with the tissue being mounted over the frame immediately prior to use.