- The non-linear dynamic equations of the first-order shear deformation theory and the third-order shear deformation plate theory of Reddy are reformulated into equations describing the interior and edge-zone problems of rectangular plates. Viscous damping terms are also included. It is shown that, for certain boundary conditions, the number of governing equations can be reduced to three, as in the classical plate theory. Two problems related to static large-deflection and dynamic small-deflection of rectangular plates are considered. Numerical results are presented to demonstrate the effects of non-linearity, shear deformation, rotatory inertia, damping and sonic boom type loadings. 1991.