An intervertebral prosthesis for insertion by posterior approach, designed to be inserted in pairs between two vertebral bodies, said prosthesis consisting of a prosthesis body extending in a longitudinal direction of intervertebral insertion, including peripheral faces delimiting, on the inside, an inner space for receiving a bone substitute. The prosthesis includes a prosthesis body of which the lower and upper bearing faces have a convex profile having continuously variable convexity in the longitudinal direction. The invention is intended for the treatment of individuals suffering from disc degeneration in the thoracic or lumbar vertebrae.