A method, and devices for facilitating the method, for shoulder replacement surgery. The method entails establishing a mechanical support in a the anatomical neck plane of the proximal humeral head, fixing a jig to the mechanical support, where the jig supports a drill guide with its axis perpendicular to the anatomical neck plane, adjusting the drill guide it coincide with the axis of the humeral head, drilling a hole through the humeral head for insertion of a shaft which will support and rotate a reaming bit. The reaming bits used to resurface the humeral head and the glenoid fossa are inserted through the back of the patient, through a gap created between two easily separated muscles, rather than through a gap cut through the subscapularis muscle on the front of the joint. A suitable jig is provided to facilitate the method.