A modular humeral prosthesis for replacement of the humeral head of a humerus. The prosthesis generally comprises a stem to be fitted to a resected humerus; a head sized and configured to approximate the humeral head; and an intermediate connecting member for connecting the stem to the head. The intermediate connecting member provides a desired angle of inclination or offset between stem and head. The head may be a traditional humeral head, or it may be an eccentric humeral head, with its mating portion being offset. The head may also comprise a groove or milled trench at least partially surrounding or otherwise defining mating portion. Also disclosed is a modular humeral prosthesis kit comprising a variety of different intermediate connecting members that may be selected to tit the prosthesis to the patient, and a method of replacing a humeral head in a patient.