An endoprosthetic scapular glenoid component is provided with a concave bearing surface of elongated part-spherical shape significantly less than hemispherical extent. The surface forms the larger end face of a generally frusto-pyramidal body of which the side faces have a relieved structure for fixation in the scapular with gap-filling cement. The pyramidal body is preferably quadrilateral with two opposed planar side faces and the other two convexly rounded. For use in a total shoulder joint device, the glenoid component can be associated with a variety of generally spherically headed, intramedullary stemmed, humeral components. Preferably the humeral component head is of minor segmental form, and the stem inclined relative to the head over a major free end portion of its length.