An intervertebral disk prosthesis, having a rigid top plate, a rigid bottom plate, and an elastically deformable intermediate cushion housed between the two inner surfaces of the plates. The cushion, at rest, possesses a wedge-shape possessing at least one front notch open into the larger end of the wedge and one rear notch open into the narrower end. The faces of the notches co-operate by contact over an area of magnitude that varies as a function of the intensity and/or direction of the load to which the prosthesis is subjected. The bottoms of the notches are spaced apart from each other and situated in the narrower half of the prosthesis.