- The analytical frequency and buckling equations of rectangular plates with various boundary conditions are developed using the interior and the edge-zone equations associated with the first-order shear deformation plate theory. The plates are laminated of transversely isotropic layers. It is shown that the solution contribution of the edge-zone equation on the natural frequency and the buckling load is negligible. Numerical results are developed and compared with the third-order shear deformation plate theories of Levinson and Reddy. 1992 Springer-Verlag.