Analysis and numerical results for the axisymmetric vibrations of two-directional functionally graded circular plates under the action of an in-plane force have been presented on the basis of classical theory of plates. The mechanical properties of the plate material are assumed to vary in both radial and transverse directions. Generalized differential quadrature method has been employed to obtain the frequency equations from the differential equation governing the motion of such simply supported and clamped plates. The lowest three roots of these frequency equations have been reported as the first three modes of vibration. The effect of volume fraction index, in-plane force parameter, heterogeneity parameter and density parameter has been studied on the natural frequencies of vibration. By allowing the frequencies to approach zero, the critical buckling loads for both the plates have been computed. Three-dimensional (3D) mode shapes for specified plate have been plotted. A comparison of results has been presented.