This set (J) comprises glenoid components (S1, S2, M1, M2, L1, L2) that each include a body (S1.1, S2.1, M1.1, M2.1, L1.1, L2.1) defining, on two of its opposite faces, respectively, a joint surface (S1.2, S2.2, M1.2, M2.2, L1.2, L2.2), intended to cooperate with a humeral head, and a bearing surface (S1.3, S2.3, M1.3, M2.3, L1.3, L2.3) bearing against the socket of a shoulder blade. In this set, the glenoid components are provided in several different sizes (S, M, L), respectively defined by the dimensions of the joint surface of their body. At least two glenoid components (S1 and S2, M1 and M2, L1 and L2) of which the bearing surfaces (S1.3 and S2.3, M1.3 and M2.3, L1.3 and L2.3) respectively have different dimensional geometries are provided so as to allow the surgeon to improve the durability of the mechanical cooperation between the implanted component and the operated socket.
