Abstract: In this paper, by developing the complex Fourier series method to solve the boundary value problem of a system of partial differential equations with constant coefficients, for the first time a general analytic solution satisfying an arbitrary boundary condition is presented for the elastic bending of thick Reissner plates in engineering. The solution is simple and convenient to programming. Analysis and computation are performed for the uniformly loaded plates under two different supporting conditions(four simply supported edges or three clamped and one free edges), the results of which are fairly satisfactory in comparison wit h those available for reference. And at the same time the analytic solution has been investigated mainly in three aspects:a) speed of convergence; b) reliability(rationality); c)fitting of boundary conditions.