The current work deals with the determination of stress and deflection of fiber-reinforced composite plates in static condition and the frequencies of free vibration of laminated plates and central deflections of isotropic, orthotropic, and sandwich composite plates in transient condition using flat facet shell element through ABAQUS. The obtained results compare with the 3D elasticity solution, Higher-Order Shear Deformation Theory (HOST), and experimental results. Further comparative studies on the parametric effects of mesh size and aspect ratio on the stress analysis of plates are studied for static and transient dynamic response. Investigations on the effect of natural frequencies, mesh size, aspect ratio, critical time step, and conditional stability on the central deflection of plate concerning time steps are also studied. The non-dimensionalized natural frequencies of laminated plates subjected to varying boundary conditions and loading, in free vibration are in close agreement with 3D elastic solutions. Findings tell us that ABACUS gives comparable results.