This set comprises glenoid components that each include a body defining, on two of its opposite faces, respectively, a joint surface, intended to cooperate with a humeral head, and a bearing surface bearing against the socket of a shoulder blade. In this set, the glenoid components are provided in several different sizes, respectively defined by the dimensions of the joint surface of their body. At least two glenoid components of which the bearing surfaces 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.