A set of surgical instruments for fitting an inverted shoulder prosthesis, which includes: - an instrument (60; 160) for shaping the bone matter making up the upper humeral epiphysis of a humerus, in a one-piece volume (E 3) that extends lengthwise around an axis (E X-X) inclined relative to the longitudinal direction of the humerus, and - an instrument (70; 170) for cutting the humeral epiphysis shaped by the shaping instrument (60; 160), to cut the volume of bone matter (E 3) transversely to the axis (E X-X) of that volume, said cutting instrument including: (a) a tubular block suitable for being slipped around the volume of the material (E 3) shaped by the shaping instrument, that tubular block delimiting, at its longitudinal end turned during use toward the humerus, a transverse slot for the passage of a saw blade or similar member, to cut the volume of bone matter (E 3) along a first plane (E 4) transverse to the axis (E X-X) of the volume, or (b) an annular body suitable for being mounted around the humeral epiphysis while surrounding both the volume of bone matter (E 3) shaped by the shaping instrument and at least a part of the rest of the humeral epiphysis, the annular body delimiting, at its side turned during use toward the humerus, a guide surface for a bone cutting tool, to cut at least the volume of bone matter (E 3) transversely to its axis (E X-X), this tubular block and this annular body thus making it possible to free the volume of bone matter from the humerus such that it forms a graft for lateralizing a glenoid component of the inverted shoulder prosthesis from the scapula of a patient to be provided with this prosthesis. - an instrument (60; 160) for shaping the bone matter making up the upper humeral epiphysis of a humerus, in a one-piece volume (E 3) that extends lengthwise around an axis (E X-X) inclined relative to the longitudinal direction of the humerus, and - an instrument (70; 170) for cutting the humeral epiphysis shaped by the shaping instrument (60; 160), to cut the volume of bone matter (E 3) transversely to the axis (E X-X) of that volume, said cutting instrument including: (a) a tubular block suitable for being slipped around the volume of the material (E 3) shaped by the shaping instrument, that tubular block delimiting, at its longitudinal end turned during use toward the humerus, a transverse slot for the passage of a saw blade or similar member, to cut the volume of bone matter (E 3) along a first plane (E 4) transverse to the axis (E X-X) of the volume, or (b) an annular body suitable for being mounted around the humeral epiphysis while surrounding both the volume of bone matter (E 3) shaped by the shaping instrument and at least a part of the rest of the humeral epiphysis, (a) a tubular block suitable for being slipped around the volume of the material (E 3) shaped by the shaping instrument, that tubular block delimiting, at its longitudinal end turned during use toward the humerus, a transverse slot for the passage of a saw blade or similar member, to cut the volume of bone matter (E 3) along a first plane (E 4) transverse to the axis (E X-X) of the volume, or (b) an annular body suitable for being mounted around the humeral epiphysis while surrounding both the volume of bone matter (E 3) shaped by the shaping instrument and at least a part of the rest of the humeral epiphysis,