The problem of a piezoelectric body with a cylindrical cavity is studied within the framework of the 3D exact equations of electro-elasticity theory using Hamilton's principle. It is supposed that the plate has simply-supported, mechanical and short-circuit conditions with respect to the electric potential along all its lateral edge surfaces. The solution to the corresponding free vibration problems is determined numerically by 3D FEM with the help of programs and algorithms composed by the authors. This paper successfully identifies the hole (cavity) size, volume fraction and location in finite piezoelectric plates as well as the coupling effect between the mechanical and electrical fields on the natural frequencies. The numerical results that confirm the effectiveness of the proposed method for cavity identification in piezoelectric plates are presented in detail.