This shoulder prosthesis, comprising a glenoid element (6) intended to be attached to the scapula. According to the invention, this glenoid element (6) comprises a distal anchoring tail (20) and a proximal flange (21), the distal anchoring tail (20) having a substantially "I-shaped" cross-section, i.e. with a central core and two side walls substantially perpendicular to this central core, and with a helicoidally twisted shape, and the proximal flange (21) being perforated with at least one hole (30); and the prosthesis comprises at least one screw (5) intended to be engaged into the hole (30) of said flange (21) and inserted into the bone.