A modular hip prosthesis can be custom fitted to a particular patient by a surgeon prior to surgical insertion. The prosthesis features a body having a neck portion for carrying a rounded head element, a transitional mid-section of the prosthesis body includes generally rectangular and generally rounded cross-sectional areas, and a stem section has a generally rounded cross-sectional area. The stem is tapered to receive a tubular extension sleeve with a hollowed portion corresponding in shape to the stem portion of the prosthesis. The tubular extension sleeve has an open end portion receptive of the lower tapering stem of the prosthesis body. The stem portion including an internal bore, and an attachment in the form of an elongated screw is provided for connection to the stem internal bore for securing the extension sleeve and the prosthesis body together, forming a compressive sealed connection therebetween. Pads can be attached to the transitional mid-section of the prosthesis body for increasing the cross-sectional shape of the prosthesis at the transitional mid-section. Removable collars can be added to the prosthesis to form a transverse load carrying interface with the upper end of the patient's femur. Frustro-conically shaped extension sleeves can be added to the prosthesis neck for extending the neck length.