Packages of thin-layered rubber-metal elements (TRME) are successfully used as bearings, joints, compensating devices, vibration and shock absorbers etc. TRME significantly outperform the traditional elements of the same purpose because of their reliability, low cost, simplicity of structural layout and assembly. TRME packages usually work under heavy compressive loads. TRME have high compression stiffness, which are several orders of magnitude greater than their shear stiffness. With the compressive forces increasing shear stiffness of such packets is reduced which leads to a loss of buckling stability. For TRME package under compression, unlike the classical theory of rod buckling stability, the shear instability takes place. In this paper bucling of flat-type TRME packages of rectangular shape under compression is discussed. The next formulas are derived for package design: the dependence of the critical external loads on loading conditions, on packages endfixity conditions, on layers geometrical parameters and mechanical properties of layers materials. The dependence of mechanical modules of elastomeric on the compressive load level is taken into account. It is assumed that the non-elastomeric layers are either perfectly rigid, or may undergo only a plane tensile strain. Small deformation is considered. The solutions obtained are compared with experimental data of other authors.