A higher order theory for bending of homogeneous orthotropic elastic plates has been developed in the preceding paper. In the present paper, the theory is applied to some illustrative problems to test its accuracy and usefulness in comparison with the Reissner type theory and classical theory. Two problems are selected; (1) cylindrical bending of a simply supported rectangular plate of infinite length due to lateral pressure, and (2) bending of a simply supported rectangular plate due to sinusoidal pressure. These problems have been being used as benchmark problems because exact solutions of three-dimensional elasticity can be calculated without much difficulty. The results of the numerical calculations show that the higher order theory is much superior in the accuracy to other plate theories. As far as the stresses are concerned, an excellent agreement is observed between the higher order theory and elasticity solutions in broad range of geometric parameters.