In this paper, the dynamics of functionally graded plates resting on elastic foundation is investigated using finite element method. The properties of the plate material like modulus of elasticity and material density are considered to be varying exponentially along the axial direction. The elastic foundation is of Winkler type which is modelled as a combination of evenly spaced linear elastic springs. The formulation of the plate is based on the Mindlin plate theory where the effect of rotary inertia and shear deformation are incorporated. The governing equations for the free vibration problem are derived from Hamilton's principle. Two discrete boundary conditions viz. all sides clamped and all sides simply supported are considered. The results of the present methodology are compared with already established results in the literature and good agreement is observed. The effect of different parameters like foundation stiffness and material variation parameter is reported. It is found that the natural frequency of the plate increases with increasing foundation stiffness which suggests that the elastic foundation adds to the stiffness of the system.