In practice, circular and annular plates usually have intermediate supports, and are eccentrically attached with subsystems due to their limited space. In order to analyze the vibration characteristics o f the plates, the integral equation method is adopted. By using the theory of sp ecial functions, Fourier Bessel function and Green function constructed from a complete set of ort hornormal funcitons of the space of squareintegrable funtims L2（a,b）consisting of Bessel functions of the first and the second kind,the free vibraction problem of the plates is transformed into the eigenvalue problem of the integral equation, and then into a standard eigenvalue problem of a matrix with infinite order.Calculated results show the effectiveness and feasibility of the method. Not only the method is simple and quick, but it can be used to analyze the non axial symmetric vibration of circular and annular plates attached with substruct ures as a whole, thus providing an effective way for the optimal design and safe ty evaluation of structures of this kind.