Free vibration analysis of plates made of functionally graded materials and resting on elastic foundation is presented by taking into account the effect of transverse shear deformations. The foundation is described by the Pasternak (two-parameter) model. The material properties of the plate are assumed to vary continuously in the thickness direction by a simple power law distribution in terms of the volume fractions of the constituents. The formulation is based on a higher order hyperbolic shear deformation theory. The equation of motion for thick functionally graded plates is obtained through the Hamilton's principle. The closed form solutions are obtained by using Navier technique and then fundamental frequencies are found by solving the results of eigenvalue problems. Accuracy of the present formulation is shown by comparing the results of numerical examples with the ones available in literature. (C) 2013 Elsevier Ltd. All rights reserved.