Combined the integral representations for displacements of semi-infinite elastic foundation subjected to arbitrary vertical dead load with the bending analytic solution of an elastic rectangle plate with four free edges rested on semi-infinite elastic foundation to develop an efficient calculating technique used to resolve the foundation displacements. Based on carrying on a great quantity of numerical calculation analysis of some instances

the displacement distributed regularities are given for the foundation beneath the plate with four free edges rested on semi-infinite elastic foundation along the foundation depth. Based on the distributed disciplinarians of foundations’ horizontal displacement and vertical displacement

proposed the assumptions that the foundations’ displacements change according to the specified functional relation along the depth. Considered horizontal displacement of the foundation beneath the plate

utilized the plate and foundation system’s principle of minimum potential energy

operated by means of the variational principles

and gave out the refined model for plates on elastic foundations. This model is reduced to double-parameter model under not considering the foundations’ horizontal displacement beneath the plate. The approximate boundary conditions of plates on this refined model of foundations are given.