This investigation considers the problem of deflection and strength of the rectangular plate with elastic hinges and splits under general distribution of loading, and under the boundary conditions in which one pair of opposite edges normal to the direction of elastic hinges and splits are simply supported, the other pair of edges are elastically supported or elastically built-in. We express the influence of elastic hinges on the rectangular plate in impulse function of 3rd order, and that of splits on the plate in impulse function of 4th. order. And we apply double finite Fourier Transformation to solve the equation of equilibrium of the rectangurar plate under the above boundary conditions.