A workpiece will be subject to gravity and cutting forces during the machining operation. In order to resist external loads, multiple clamping forces are usually exerted on a workpiece so that it can be hold to be the correct position during the entire machining operation. However, insufficient clamping forces cannot prevent the workpiece from motions whereas excessive clamping forces may cause the improper deformations of workpiece-fixture system. Therefore, a systematic determination of magnitudes and placements of clamping forces is formulated as nonlinear constrained equations according to the minimum total complementary energy. By solving the resulting nonlinear equations, all contact forces including clamping forces and their application placements can accurately predicted in the frictional workpiece-fixture system. This method is illustrated with example cases.