Research on geometrically nonlinear static and dynamic problems of composite plates has so far produced several approximate solutions. Most of these solutions are based on an assumed single-mode approximation. Since closed-form solutions do not exist for many of these nonlinear problems, it is almost impossible to evaluate the accuracy of these approximate solutions. A method is presented in this paper by which approximate solutions can be compared and improved results can be generated for certain geometrically nonlinear problems concerning composite plates. Self-Generating Functions of zero, first and second order are used to obtain the numerical results. The effects of amplitude, geometry and material constants on the dynamic behavior of composite plates are investigated with the aid of some examples.