First, the theorem on energy of higher order velocity of the holonomic potential mechanical system is presented with on explaining of the physical meaning of energy of higher order velocity of the system. The general criterion of potential mechanical system is then presented. On this basis, the higher order Lagrange function is introduced,the higher order Lagrange equations of holonomic potential mechanical system are derived, and the higher order cyclic integral and the integral of higher order generalized energy of the system are obtained.