The effects of a cutout or hole inside a freely vibrating rectangular plate on the dynamics of an elastic plate are investigated. A general superellipse representation is employed to describe the boundary shape of the cutout, and a general FE analyzer ANSYS is used to evaluate the natural frequencies of the perforated plate. Numerical results show that the plate frequencies are highly dependent upon the shape, size, position and orientation of the cutout. Moreover, the effect is also highly related to the boundary conditions of the plate. In a practical engineering application, the design of a cutout within a thin rectangular plate deserves careful consideration so as to control the dynamic behaviors of the plate.