Abstract: With the help of Conformal Mapping theory, trigonometric interpolation method between odd and even sequences in rectangle boundary regions is used, and the conformal mapping function between unit dish region and complicated region such as rectangle-plates with arc radius is carried out. Aiming at determining the fundamental vibrating frequency of a special-shaped, simple-supported elastic rectangle-plate, in the in-plane state of constant stress, the vibration function of this complicated plate is obtained by unit dish region, and the coefficient of fundamental frequency are analyzed. Using simple-supported elastic rectangle-plates with arc radius as an example, the effects on fundamental frequency caused by the concentrated mass and position, the ratio between the width and length of rectangle-plates, as well as the coefficient Sp of constant in-plane stress are analyzed respectively.