The instant invention provides a modular shoulder prosthesis. The prosthesis includes an intramedullary rod element which is to be inserted in a bone. The proximal portion of the rod includes a self-holding taper which is telescoped into one end of a bore in the body element. The mating tapered surfaces of the rod and the body bore form a rotationally movable connection. Whereby the body of the prosthesis may be rotationally positioned after insertion of the rod. A neck element having a shaped protrusion is telescoped into a cavity in the other end of the body bore to prevent rotational movement therebetween. A threaded fastener provides a drawing force to lock all of the components together into a fixed orientation.