An analytical theory of the finite element method discussed in [1,2], is implemented here for the plane stress state of the rectangular plate. Its finite element model composed of identical rectangular finite elements with the same approximation in the displacements, is interpreted as a regular elastic system. Using the discrete-continuous analysis developed in [3-5], a discrete two-dimensional closed linear theory is built in terms of the nodal displacements and generalized strains, internal and external forces of the elements – functions of two integer arguments used for numbering the elements of the system. Within the constructed theory alternative formulations of problems and exact analytical solutions of some of them are given.