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 fit the prosthesis to the patient , and a method of replacing a humeral head in a patient .