In this paper, by developing the complex Fourier series method to solve theboundary value problem of a system of partial differential equations with constantcoefficients, for the first time a general analytic solution satisfying an arbitraryboundary condition is presented for the elastic bending of thick Reissuer plates inengineering. The solution is simple and convenient to programming. Analysis andcomputation are performed for the uniformly loaded plates under two differentsupporting conditions (four simply. supported edges or three clamped and one freeedges), the results of which are fairly satisfactory in comparison Mwth those availablefor reference. And at the some time the analytic solution has been invesligated mainlyin three aspects: a) speed of convergence. b) reliability (rationality), c) fitting ofboundary conditions. In this paper, by developing the complex Fourier series method to solve theboundary value problem of a system of partial differential equations with constantcoefficients, for the first time a general analytic solution satisfying an arbitraryboundary condition is presented for the elastic bending of thick Reissuer plates inengineering. Analysis andcomputation are performed for the uniformly loaded plates under two differentsupporting conditions (four simply. Supported edges or three clamped and one freeedges), the results of which are fairly satisfactory in comparison Mwth those available for reference. A) speed of convergence. B) reliability (rationality), c) fitting ofboundary conditions.