Abstract: In order to calculate the fundamental vibration frequency of special-shaped, elastic clamped-plates, conformal mapping theory is used to separate the interpolating points of complicated boundary into odd and even sequences, both of which can be iterated mutually, so that the conformal mapping function between the complicated region and the unit dish region can be established. Trigonometric interpolation and its convergence along normal direction are provided. The complex coefficients of the conformal mapping function are then calculated. Furthermore, by using Galerkin method, the solution of the fundamental frequency of the complicated vibrating region is achieved. Finally, an ellipse elastic clamped-plate is used as an example to analyze the effects on fundamental frequency coefficient caused by eccentric ratio e and area size.