Buckling modes of a linearly elastic compressed medium are discussed. Stability of a plate lying on a soft elastic foundation is investigated. To the plate surface a membrane with initial stresses is attached. The stresses in the membrane simulate difference of equilibrium distances between atoms of crystal lattices of a surface layer (membrane) and of a plate. Also the influence of force and thermal stresses is studied. The chessboard-like stable buckling mode appears on the membrane surface at the stability loss. The ways of control of the wave length of buckling mode are discussed.