An analytical solution based on the neutral surface concept is developed to study the free vibration behavior of a simply supported functionally graded plate reposing on the elastic foundation by taking into account the effect of transverse shear deformations. No transversal shear correction factors are needed because a correct representation of the transversal shearing strain obtained by using a new refined shear deformation theory. The foundation is described by the Winkler–Pasternak model. The Young's modulus of the plate is assumed to vary continuously through the thickness according to a power law formulation, and the Poisson ratio is held constant. The equation of motion for FG rectangular plates resting on an elastic foundation is obtained through Hamilton's principle. Numerical examples are provided to show the effect of foundation stiffness parameters presented for thick to thin plates and for various values of the gradient index, aspect, and the side-to-thickness ratio. It was found that the proposed theory predicts the fundamental frequencies very well, consistently with those available in the literature.