Based on Reissner’s sandwich plate theory,the nonlinear dynamic equations of the circular sandwich plate under static load are established by using the Hamilton principle. The axisymmetric nonlinear vibration differential equation of the plate under static load is obtained by Galerkin method. The amplitude-frequency response equation of the primary resonance system is solved by means of a method of multiple scales,and the stability criterion of the steady motion of the system is obtained based on the Lyapunov stability theory. Through the numerical example,the amplitude-frequency response curves of primary resonance of the system with simply supported edge are obtained. The curves of the amplitude varying with static load,excitation and thickness of the core layer are plotted,respectively. The effects of different parameters on the resonance amplitude are discussed,and the stability of steady-state motions of the system is analyzed.