First – order orthotropic shear deformation equations for the nonlinearly elastic bending response of rectangular plates are introduced. Their solution using a computer program based on finite differences implementation of the Dynamic Relaxation (DR) method is outlined. The convergence and accuracy of the DR solutions for elastic large deflection response of isotropic, orthotropic, and laminated plates are established by comparison with various exact and approximate solutions. The present Dynamic Relaxation method (DR) coupled with finite differences method shows a fairly good agreement with other analytical and numerical methods used in the verification scheme. It was found that: The convergence and accuracy of the DR solution are dependent on several factors including boundary conditions, mesh size and type, fictitious densities, damping coefficients, time increment and applied load. Also, the DR large deflection program using uniform finite differences meshes can be employed in the analysis of different thicknesses for isotropic, orthotropic or laminated plates under uniform loads. All the comparison results for simply supported (SS4) edge conditions showed that deflection is almost dependent on the direction of the applied load or the arrangement of the layers.