Abstract: According to the structural characteristics of the end-shield of electric machines, an end-shield can be simplified as an annular circular plate. Based on the theory of elasticity, the vibration equation of the circular plate is established. Using Galerkin’s method by introducing a modal function, the nonlinear vibration equation of the end-shield with 5 kinds boundary conditions is obtained. By means of the method of mutipul scales for nonlinear vibrations, the approximation solution for superharmonic resonance of a system is obtained. Amplitude frequency response curves of 5 kinds of boundary conditions of a superharmonic resonance system are derived. The numerical analysis on the influence of the radius and excitation of the amplitude frequency response curves of the system is carried out.