A prosthetic glenoid component for attachment to a scapula to provide a bearing for a humeral head in a shoulder prosthesis has a one-piece bearing element having a concave lateral bearing surface for contact with the humeral head with which it is to be used. An opposing relatively hard medial surface of the bearing element is provided for attachment to a scapula. The lateral surface is a soft low modulus concave lateral bearing surface extends around the periphery of the bearing element and increases its thickness to provide a deformable rim to simulate the labrum in an anatomical glenoid. The bearing element preferably has two affixation pegs which project from the medial face thereof, one at a superior position which projects in a superior direction and the other which is located in an inferior position and which projects in an inferior direction which is angled in relation to the medial-lateral direction.