A knee replacement prosthesis comprising a femoral component and a tibial component that enable anterior-posterior translation of the femur relative to the tibia and enable the tibia to rotate about its longitudinal axis during flexion of the knee. The femoral component connects to the distal end of a resected femur and includes medial and lateral condyles having distal, articulating surfaces, and a patellar flange having a patellar articulating surface. The tibial component connects to the proximal end of a resected tibia and includes a proximal bearing surface with medial and lateral concavities that articulate with the medial and lateral condyles. The condylar articulating surfaces and the said concavities are substantially defined by non-uniform, rational B-spline surfaces (NURBS).