Rectangular plates with variable geometric and mechanic characteristics have been used widely in various industries. Transversally loaded rectangular plate can rest on elastic foundation, as in, for example, surfaces of roads, bridge or airport runways. Knowledge of stressstrain state is essential for researching of strength and load bearing capacity of such constructions. In this paper, we use a method of collocations and least residuals to find numerical solution of plate bending problem. The method of collocations and least residuals has proved to be effective for ordinary differential equations and partial differential equation of hydrodynamics. However, it is used for the first time for plate stress-strain state calculation. The problem of stress-strain state calculation for isotropic rectangular plates on elastic foundation and for plates free-lying on the ground has been solved. Special boundary conditions for plate with free boundaries are used. Several models of foundation reaction are considered, and qualitative comparison of obtained results is provided.