This paper presents an analytical-numerical methodology for the geometrically nonlinear analysis of laminated composite plates under dynamic loading. The methodology employs Galerkin technique, in which suitable polynomials are chosen as trial functions. In the solution process, Newmark's scheme for time integration, and modified Newton-Raphson method for the solution of resulting nonlinear equations are used. In the formulation, first order shear deformation theory based on Mindlin's hypothesis and von Karman type geometric nonlinearity are considered. The results are compared to that of finite strips, and Chebyshev series published elsewhere. The method is found to determine closely both the displacements and the stresses. A finite element analysis has also been carried out for the validation of the results. The present method can be efficiently and easily applied for the nonlinear transient analysis of laminated composite plates with various boundary conditions.