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In this study, free vibration analysis of Reissner plates on Pasternak foundation is carried outby mixed finite element method based on the Geaux differential. New boundary conditions areestablished for plates on Pasternak foundation. This method is developed and applied to numerousproblems by Ak and his co-workers. In dynamic analysis, the problem reduces to the solution of astandard 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 anddisplacements are the basic unknowns. The element performance is assessed by comparison withnumerical examples known from literature. Validity limits of Kirchhoff plate theory is tested by dynamicanalysis. Shear locking effects are tested as far as h/2a=10-6 and it is observed that REC32 is free fromshear locking.