Prosthesis for inserting into a damaged intervertebral disc. The prosthesis has an elongated tubular main prosthesis body with a length to fit laterally from one side of a disc to the other at its mid-plane. The main prosthesis body is composed of two parts transversely oriented and has a vertical height deliberately greater than the height of normal disc space. Heads having a vertical height greater than the vertical height of the main prosthesis body are mounted on the ends of the main prosthesis body.