Abstract: A head for a modular humeral (or hip) prosthesis which mates couplingly to a head mounting seat on the end of on elongated humeral stem is described. The head has an enganing syherical shaped outer surface which has a radius measured from a center which lies along an offset line which is inclined at an angle which ranges from between 10 to 30 degrees from the normal longitudinal axis of the elongated stem. The head has a longitudinal axis which is shifted form between 2.5 to 7.5 mm from a normal longitudinal axis. The elongated humeral stem includes a shaft seat which passes through the head mounting seat, which is adapted to receive a shaft extending from head. An adjustable to receive a shaft extending from the head. An adjustable interlocking alignment pin ensures desired orientation between the head and the head mounting seat during mating of the parts and maintains stability of orientation when mated.