A reverse joint prosthesis to replace a “ball and socket” joint such as a hip or shoulder. In the case of a hip, the prosthesis comprises an acetabular cup for implanting in an acetabular socket. The acetabular cup is secured to the acetabular socket of the pelvis. The acetabular cup has a stem extending from the center of a concave portion thereof and an acetabular ball is attached to the stem. A femoral implant is provided with a femoral cup attached to the proximal end thereof. The femoral cup has a stem which can be constructed in a modular fashion with several stem lengths to accommodate different size patients. After implantation of the acetabular cup and ball and the femoral cup, the members are assembled together so that the femoral cup can articulate on the acetabular ball. The prosthesis of the invention has substantially reduced likelihood of dislocation during extreme ranges of motion.