Dynamic Relaxation (DR) method is presented for the geometrically nonlinear laterally loaded, rectangular laminated plates. The analysis uses the Mindlin plate theory which accounts for transverse shear deformation. A computer program has been compiled. The convergence and accuracy of the DR solutions for elastic large deflection response are established by comparison with various exact and approximate solutions. New numerical results are generated for uniformly loaded square laminated plates which serve to quantify the effects of shear deformation, length to thickness ratio, number of layers, material anisotropy and fiber orientation. It was found that linear analysis seriously over predicts deflection of plates. The shear deflection depends greatly on a number of factors such as length to thickness ratio, degree of anisotropy and number of layers. As the degree of anisotropy increases, the plate becomes stiffer and when it is greater than a critical value, the deflection becomes virtually independent on the degree of anisotropy. It was also found that deflection of plates depends on the angle of orientation of individual plies and the size of load applied.