An approach is presented for the vibration analysis of annular, confocal, elliptic plate. The approach employs the separation of variables, finite difference, and receptance concept. This method is then expanded to square plate with center crack, or with more complex geometries. The basic idea of this paper is: split the plate into several strips and get the strips’ characteristic values, then compose these strips by the receptance method to get the characteristics value of the plate. Numerical results for certain cases are compared to known data, and precise agreement is met.