Abstract: In the context of hydromechanics and elasticity, nonlinear vibration equations of cylindrical shell of coupling system are established. Using the average method, the first approximate analytical solution of nonlinear vibration equations with four degrees of freedom is obtained. For low frequency & large magnitude rotating gravity wave, this paper develops the relationship between its amplitude and vibration properties of exciting forces, thus the dynamic characters of nonlinear vibration system are analyzed. The approximate analytical solution is basically consistent with the numerical solution and experimental phenomena.