A spinal disc prosthesis (10) to replace a damaged spinal disc in a spinal column (16) of a human, includes an elastomeric core (200) having upper and lower surfaces (202, 212) which are parallel to each other. An upper rigid plate (20) has opposed first and second surfaces (42, 52). The first surface (42) is affixed to the upper surface (202) of the elastomeric core. The second surface (52) is inclined relative to the first surface (42). A lower rigid plate (120) has opposed third and fourth surfaces (142, 152). The third surface (142) is affixed to the lower surface (212) of the elastomeric core (200) and extends parallel to the first surface (42). The fourth surface (152) is inclined relative to the third surface (142). The second and fourth surfaces (52, 152) are inclined relative to each other.