Stability of shock absorbers with thin-multilayered rubber-metal elements (TRME) of flat, circular shape is considered in this work. TRME packages that are used as vibration isolators usually work under heavy compressive loads, which may lead to buckling failure. Next, formulas for package design are derived: the dependence of the critical force on geometryof layer, on mechanical properties of material of elastomeric layers, on packages end-fixity conditions. The dependence of mechanical modules of elastomeric on the compressive load level is taken into account. The obtained solutions are compared to experimental data of other authors.