In this article, free vibration analysis of thick functionally graded isotropic and transversely isotropic rectangular plates are investigated. Based on the higher-order shear and normal deformable plate theory of Batra and Vidoli, the governing equations are obtained using the principle of virtual work. The equations are then solved analytically, assuming the simply support boundary condition along all edges. In higher-order shear and normal deformable plate theory, the effects of the both transverse shear and normal deformations, are considered. Advantages of this theory compared to the shear theories is that, given that deflection of the plate along the thickness is not constant, for thick plate provides more accurate results. A power law distribution is used to explain the variation of mechanical, electrical and physical properties through the thickness of the functionally graded materials. Furthermore, after showing the accuracy of present analytical approach, the numerical results for different plate parameters has been listed and the different parameters effect on the plate natural frequencies has been studied in details. This investigation is shown that when fifth-order expansion is used, the results of this theory for natural frequencies of thick functionally graded rectangular plates are very close to those obtained from three dimensional elasticity theory.