A scapula component (1) for a reverse shoulder prosthesis comprises a part spherical, convex, surface (3) which is less than a hemisphere. The part spherical surface does not have a rotational axis of symmetry, and may include a main circular surface portion and one or more subsidiary surface portions (5, 6, 7) depending from an edge of the main surface portion. A humerus component (200) for a reverse shoulder prosthesis comprises a cup member (202) having a part spherical, concave bearing surface (206) surrounded by an oval rim (208).