Apparatus for delivering stents to body lumens include a flexible catheter shaft, an expandable member, a tubular prosthesis selectively movable in an axial direction over the expandable member, and a stop member disposed on the catheter shaft near the distal end of the catheter shaft for stopping the prosthesis at a deployment position on the expandable member. A variety of different stop members are provided according to various embodiments, such as stop members disposed outside the expandable member, stop members disposed inside the expandable member, movable stop members, and the like. Methods of delivering stents are also provided.