A surgical apparatus for implanting a glenoid component of a shoulder prosthesis, the apparatus comprising:
- position-finding means for spatially locating a scapula of a patient;
- mapping means for mapping a glenoid surface of the scapula;
- modeling means for implementing the modeling method of claim 1 and thereby obtaining a theoretical glenoid surface from cartographic data of the glenoid surface supplied by the mapping means;
- first means of determination for determining a spatial position of a lower reference point for implanting the glenoid component from the cartographic data obtained at a lower end of the glenoid surface by the mapping means;
- and
- means of implantation for obtaining a spatial implantation configuration of the glenoid component from at least the theoretical glenoid surface and the lower reference point.