In this paper, free vibration of two-dimensional functionally graded (2D-FG) annular sectorial plate surrounded by Winkler-Pasternak elastic foundation has been investigated. It is assumed that the plate properties vary continuously through its both circumference and thickness according to power law distribution of the volume fraction. Primarily, we calculate the forces and resultant moments and then the total potential energy of system. Then, by applying the Hamilton’s principal any by regarding the first order shear deformation plate theory (FSDT) the governing differential equations have been derived. The numerical differential quadrature method, (DQM), has been employed for solving the motion equations. Two different boundary conditions such as simply supported and clamp-simply supported are considered. Initially, the obtained results were verified against those given in the literature and by ANSYS software and we confident from the obtain results. The effects of geometrical and elastic foundation parameters along with FG power indices effects on the natural frequencies have been studied. The study of results shows that, elastic foundation and FG parameters have significant effects on natural frequencies. By doing this research for 2D-FG materials the characteristic vibration of structure can be controlled by more parameters than 1D-FG materials.