A nonlinear finite element method is adopted for the large displacement elastic-plastic dynamic analysis of anisotropic plates under in-plane compressive loads. The analysis is based on the two-dimensional layered approach with classical and higher order shear deformation theory with five, seven, and nine degrees of freedom per node, nine-node Lagrangian isoparametric quadrilateral elements are used for the discretization of the laminated plates. Both consistent and lumped mass matrices are used in the present study. Damping property is considered by using Rayleigh type damping which is linearly related to the mass and the stiffness matrices. Newmark integration method is used for solving the dynamic equilibrium equations. The effects of initial imperfection, orthotropy of individual layers, fiber’s orientation angle, type of loading, damping factor, and fiber waviness on the large displacement elastic-plastic dynamic analysis are considered. The conclusion it is shown that the antisymmetric cross-ply laminated plate has a damping rate faster than the symmetric cross-ply laminated plate and if damping is considered and if the response of the plate shows no oscillation about the static deflection position, it means that the damping factor is below the critical damping factor.