In this study, the non-linear bending analysis of isotropic and orthotropic rectangular plates is performed by Dynamic Relaxation (DR) method. In order to model the plate, the four-variable refined plate theory, which is a new and simple higher-order shear deformation theory and has a good capability in analysis of thick plates, is adopted. Despite the first-order shear deformation plate theory; this theory does not need the shear correction factor, predicts shear strains and stress parabolically across the plate thickness and satisfies the zero stress conditions on free surfaces. The governing equations are obtained using virtual work principle and the Von-Karman nonlinear terms are considered in strain-displacement equations. The non-linear coupled governing equations are solved by DR method combined with finite difference technique, and for this purpose a computer code is provided in MATLAB software. In order to demonstrate the accuracy of present method, the numerical results are compared with the existing ones and very good agreement is observed. Also the effects of side-to-thickness ratio and boundary conditions on the results are examined. Finally, the variations of shear effects by changing the plate thickness and also changing the orthotropy ratio in orthotropic plates are investigated.