Abstract: Based on analyzing the fundamental frequency of complicated elastic clamped plates subjected to in-plane constant stress, with the help of Conformal Mapping theory, interpolating points of odd and even sequence in complicated boundary region are given, and both trigonometric interpolation and normal convergence method are proposed, so that Conformal Mapping function between complicated region and the unit dish region is carried out. Then by using Galerkin method, the analysis of vibration fundamental frequency of complicated plates subjected to in-planes constant stress can be achieved. Meanwhile, using a rectangular elastic clamped plate as an example, the effect on the fundamental frequency caused by boundary length ratio λ, its area A and in-plane constant stress coefficient Sp are analyzed, respectively.