This paper addresses the free transverse vibrations of thin simply supported nonhomogeneous isotropic rectangular plates of bilinearly varying thickness with elastically restrained edges against rotation.The Gram-Schmidt process has been used to generate two-dimensional boundary characteristic orthogonal polynomials,which have been used in the Rayleigh-Ritz method to study the problem.The lowest three frequencies have been computed for various values of nonhomogeneous parameters,thickness parameters,aspect ratio and flexibility parameters.A comparison of the results with those available in the literature has been made.Three-dimensional mode shapes for the specified plate have been presented.