A system for implanting a valve prosthesis comprises a compressible and expandable stent with a collapsible and expandable valve structure mounted within the stent. An insertion catheter is provided for advancing the valve prosthesis through a small inlet opening into a body channel The valve structure is preferably formed of biological tissue. The stent may be self-expandable or may be expanded by a balloon on the distal end portion of the catheter. The stent is configured to expand in the body channel such that the outer surface of the stent engages surrounding tissue. After expansion, the valve structure within the stent becomes functional, thereby allowing blood to flow in only one direction. The valve prosthesis is detachable from the catheter for permanent implantation in the body channel. The valve prosthesis is preferably used for replacing the function of a natural heart valve without requiring open heart surgery.