In the present paper, three-dimensional elasticity solution for a functionally graded simply supported plate subjected to transverse loading is developed. The Young's modulus of the plate is assumed to vary exponentially through the thickness, and the Poisson's ratio is assumed to be constant. The approach makes use of the Plevako general solution of the equilibrium equations for inhomogeneous isotropic media. Dependence of stress and displacement fields in the plate on the inhomogeneity ratio, geometry and loading is examined and discussed. Proposed solution is validated by comparing the results for functionally graded plates to the results for a homogeneous isotropic plate.