An osteoprosthesis component which is suitable for fitting to the end of a first bone which has been resected, in a joint between that bone and a second bone, includes a transverse portion which can be fitted across the resected end of the first bone. The transverse portion has a planar first surface which faces the resected end of the first bone when the component is implanted and a second surface for engaging the second bone directly or indirectly. The component includes a rail portion around at least part of the periphery of the component extending in a direction away from the second bone, in which the inwardly facing surface of the rail portion is generally rounded extending continuously from the planar first surface of the transverse portion when the component is viewed in cross-section.