First order orthotropic shear deformation equations for the linear elastic bending response of rectangular plates are introduced. Their solution using a computer program in FORTRAN language based on finite differences implementation of the Dynamic Relaxation (DR) method is outlined. The convergence and accuracy of the DR solutions for elastic linear 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 (FD) shows a fairly good agreement with other analytical and numerical methods used in the present study. It was found that the DR linear theory program using uniform meshes can be employed in the analysis of different thicknesses and length to side ratios for isotropic, orthotropic and laminated fibrous plates under uniform loads in a fairly good accuracy. These comparisons show that the type of mesh used (i.e. uniform or graded) is responsible for the considerable variations in the mid – side and corner stress resultants. It is found that the convergence of the DR solution depends on several factors including boundary conditions, meshes size, fictitious densities and applied load. It is also found that the DR linear theory can be employed with less accuracy in the analysis of moderately thick and flat isotropic, orthotropic or laminated plates under uniform loads. It is also found that the deflection of the plate becomes of an acceptable value when the length to thickness ratio decreases. For simply supported (SS1) edge conditions, all the comparison results confirmed that deflection depends on the direction of the applied load and the arrangement of the layers.