Abstract: Using the superposition principle and equivalence principle of elastic mechanics，take the supporting system as a whole to study it，based on the priciple of energy conservation of elastic mechanics，the potential energy functions for the supporting system are derived by applying the theorem of superposition for multiple displacements under the assumption that every internal force is acting on the supporting system in turns. A new algorithm for the supporting system is also obtained by using the principle of minimum potential energy. This algorithm is simple，accurate ，and can be widely used in various types of engineering calculations.

Key words: supporting system, potential energy, displacement, principle of minimum potential energy, superposition principle