A refined theory of elastic, orthotropic plates is presented. The theory includes the effect of transverse shear deformation and normal stress and may be considered a generalization of the classical theory of von Karman modified by the refinements of the Levy-Reissner-Mindlin theories. A nonlinear system of equations is derived directly from the corresponding equations of the three-dimensional theory of elasticity in which body-force terms have been retained. Next, the system of equations is linearized and reduced to a single sixth-order partial differential equation in a stress function. A Levy-type solution of this equation is discussed.