A surgical system for implanting a glenoid component of a shoulder prosthesis, the surgical system comprising:
- position-finding means for spatially locating a scapula of a patient being operated on;
- mapping means for mapping a surface of the scapula;
- modeling means for obtaining a theoretical glenoid surface from cartographic data of the surface of the scapula supplied by the mapping means,
- first means for determining the spatial position of a lower reference point for implanting the glenoid component from the cartographic data of the surface of the scapula obtained at a location spaced away from a worn area of the glenoid by the mapping means, and
- means for obtaining a spatial implantation configuration of the glenoid component from at least the theoretical glenoid surface and the lower reference point.