Purpose <p>In this research, a 3D analytical solution is presented for free vibration analysis of simply supported thick transversely isotropic FGM plates.</p> Method <p>For this purpose, displacement components of plate are written in terms of displacement potential functions and the governing differential equations are derived by substitution of displacement components in 3D elasticity equations. The governing partial differential equations are solved using separation of variables method and employing the exact boundary conditions. The solution has no simplifying assumptions for stress, strain or displacement distribution in the plate thickness and is applicable to any plate with no limitation on its thickness ratio.</p> Results and Conclusion <p>The results are compared with other available analytical results and an excellent agreement is observed. Accurate natural frequencies are presented for different range of nonhomogeneous index, transversely isotropic material properties, and aspect and thickness ratios. The obtained results show that with an increase in nonhomogeneous index the normalized natural frequency decreases. This reduction is more noticeable for thin plates. In addition, it is observed that the effect of the nonhomogeneous index on the response of the transversely isotropic functionally graded plate increases when the shear modulus ratios decreases. Also, the results show that the influence of shear modulus ratio on the normalized frequency value increase in thick plates and its effect is more noticeable in comparison with Young modulus ratio.</p>