A unified third-order laminate plate theory that contains classical, first-order and third-order theories as special cases is presented. Analytical solutions using the Navier and L$acute{e}$vy solution procedures are presented. The Navier solutions are limited to simply supported rectangular plates while the L$acute{e}$vy solutions are restricted to rectangular plates with two parallel edges simply supported and other two edges having arbitrary combination of simply supported, clamped, and free boundary conditions. Numerical results of bending and vibration for a number of problems are discussed in the second part of the paper.