We apply the Rayleigh Ritz method to analyze multi-layered plates with residual stresses. The method is very simple, straight forward, and easily programmable, but it should be applied to structures only in simple shapes. We derive coupled variational equations based on the principle of virtual displacement, and investigate what kind of basis functions is desirable for the analysis of rectangular plates with various boundary conditions. We demonstrate the effectiveness and usefulness of the method through several examples. The analysis results obtained with the method are in good agreement with those available in literature. A multi-layered MEMS plate example shows that the coupling effect should not be ignored and that residual stresses do influence the stiffness of the structure very much.