Abstract: In this paper, the complex Fourier series method is used to solve the boundary value problem of the partial differential equation system with constant parameters. And for the first time a general analytic solution satisfying an arbitrary boundary condition is presented for the transverse bending problem of a Reissuer elastic thick plate on a ПасТернак foundation,which is evolved from the concrete apron-a widely used structure in large engineering constrUctions. The solution is in a simple form and convenient to programming. Analysis and computation are performed in three different partial loading conditions (loaded on the central part, on the middle part of one edge or on one corner part of the plate). Satisfactory results are obtained in comparison with those of other methods.