The present invention relates to an intervertebral disc prosthesis comprising at least three pieces including an upper plate, a lower plate, and a movable core at least in relation to a plate, wherein it also comprises two anatomic adaptation elements of which each has, on one hand, a surface in contact with a surface of a vertebra and, on the other hand, a face of which at least a part has a surface in contact with at least a part of the plate opposite to which the anatomic adaptation element is mounted, the anatomic adaptation elements being fixed onto the plates via fixation means.
