Summary: The objective is to develop a new complex variable boundary element method for sandwich plates of Reissner's type and Hoff's type. The general solution of Helmholtz equation in complex field is given. Based on Vekua's complex integral representation of the analytic function, the new boundary integral equations are formulated. The density function in the integral equation is determined directly by boundary element method. Some standard examples are presented, and the results of numerical solutions are accurate everywhere in the plate. The approach presented is applicable only to bounded simply connected regions.