A prosthetic heart valve implantable by catheter without surgery includes a substantially "dry" membrane or tissue material. In at least one embodiment, the tissue is folded in a dry state to form a tissue leaflet assembly that is then attached to a frame to form an implantable prosthetic heart valve. Alternatively, one or more tissue leaflets are operatively associated with a frame to form an implantable prosthetic heart valve. The implantable prosthetic heart valve is subsequently pre-mounted on an integrated catheter delivery system. The catheter delivery system that includes the implantable prosthetic heart valve is then packaged and transported while the tissue remains dry. The implantable prosthetic heart valve, while remaining substantially dry, can then be implanted into the receiving patient.