Disclosed herein are an improved tibial prosthesis and a template and reamer which are utilized in installing the prosthesis on the proximal end of a surgically prepared tibia. The prosthesis comprises a tibial component including a tray attached to the proximal tibia and an insert attached to the tray and provided to present an articulating surface for bearing engagement with the distal end of the femur or alternatively with a femoral component which has been surgically attached to the distal end of the femur. The tray includes an exterior surface including a plurality of domical contours which interengage with corresponding surfaces formed in the proximal tibia by the surgeon. The tray is preferably attached to the proximal tibia through the use of screw fasteners extending through openings formed in the domical contours. The template is utilized by the surgeon in measuring the exact location and size of the contours which are to be surgically formed in the proximal tibia. The reamer is specifically designed to enable its use during the surgical procedure to surgically create the contours which are formed in the proximal tibia.