The In experiments of liquid storage elastic shells, it has been observed that standing gravity waves with low frequency and large amplitude may be generated by excitations with very higher frequency.To explain the phenomenon, the nonlinear vibrations of liquid-filled elastic cylindrical shells coupled with sloshing free surface are investigated.First.the variational principle for the coupled nonlinear system is obtained and proved to be equal to the full set of differential equations describing the problem.Then the velocity potential, the displacement of the free surface of the liquid and the displacements of the shell are expanded into a completed set of enginfunctions, by which the Lagrangian of the system is constructed in terms of generalized coordinates.