The geometrically nonlinear analysis of laminated composite plates under dynamic loading is considered. Galerkin method with the use of Newmark's scheme in association with Newton-Raphson method is applied to obtain the dynamic nonlinear response of the plates. First order shear deformation theory based on Mindlin's hypothesis and von Karman type geometric nonlinearity are utilized. The governing differential equations are solved by choosing suitable polynomials as trial functions to approximate the plate displacements. The solutions are compared to that of Chebyshev series, finite strips and finite elements. A very close agreement has been observed with these approximating methods. In the solution process, analytical computation has been done wherever it is possible, and analytical-numerical type approach has been made for all problems.