The archwire bending is one of processes the most frequently used in the orthodontic treatment. Furthermore, the springback of sheet metal, which is defined as elastic recovery of the part during unloading, should be taken into consideration so as to produce formed archwire within acceptable tolerance limits. In this paper, the springback angle of different alloy archwires (including NiTi alloy wire, Beta-Ti alloy wires, Chinese stainless steel wires, and Australian stainless steel wires) were performed by the theoretical calculation based on large deformation theory and the finite element analysis. A series of numerical simulations has been conducted for the bending test, which physically simulates the actual bending of alloy archwire with a robotic apparatus. The finite element analysis of springback is shown to be very consistent with the theoretical calculation results.