This paper presents free vibration analysis offunctionally graded plates of different shapes withdifferent cutouts. In order to investigate the freevibration of functionally graded plates, subspacemethod is used. The material properties of the platesare assumed to vary according to a power lawdistribution in terms of the volume fraction of theconstituents. In this paper, rectangular, trapezoidal andcircular plates with cutouts are studied and the effectsof volume fraction index, thickness ratio and differentexternal boundary conditions on the naturalfrequencies of plates are studied in detail.