In this study, free vibration analysis of Reissner plates on Pasternak foundation is carried out by mixed finite element method based on the Gateaux differential. New boundary conditions are established for plates on Pasternak foundation. This method is developed and applied to numerous problems by Akoz and his co-workers. In dynamic analysis, the problem reduces to the solution of a standard eigenvalue problem and the mixed element is based upon a consistent mass matrix formulation. The element has four nodes and bending and torsional moments, transverse shear forces, rotations and displacements are the basic unknowns. The element performance is assessed by comparison with numerical examples known from literature. Validity limits of Kirchhoff plate theory is tested by dynamic analysis. Shear locking effects are tested as far as h/2a = 10(-6) and it is observed that REC32 is free from shear locking.