An orthodontic treatment planning system is described that models the effects of torque losses within an orthodontic archwire-appliance system when computing a predicted final occlusion for a dental arch. The treatment planning system models engagement of the archwire with the orthodontic appliances at each appliance position along the length of the archwire. The treatment planning system iteratively determines the twist angle of the archwire at each appliance position along the length of the archwire and incrementally adjusts the orientation and the position of each tooth based on the determined twist angles until the twist angle at each position along the archwire is within a defined tolerance of zero. When the twist angle at each position along the archwire is within a defined tolerance of zero, the archwire is relaxed and a 3D representation of the computed final occlusion of the dental arch may be displayed.