Free vibration of rectangular functionally graded material plates on different support conditions is studied based on the three-dimensional linear theory of elasticity. The three displacements of the plates are expanded by a series of Chebyshev polynomials multiplied by appropriate functions to satisfy the essential boundary conditions. The natural frequencies are obtained by the Ritz method. The present approach is validated by comparing the results with those from other theories and methods. The effects of volume fraction index, aspect ratios, and thickness-side ratios are discussed in the parametric study.