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In the article, the authors analyze main issues of protecting buildings and structures against vibroseismic effects with the help of system of elastomeric blocks, which are characterized by high vertical stiffness, low shear stiffness, high energy dissipation and ability to center vertical load; besides, they feature high reliability with no risk of sudden failure. Results of static and dynamic tests of parametric series of elastomeric blocks used for protection of residential buildings against vibrations are presented. Design of pile with anti-vibration rubber supports is described. Calculation of elastomeric blocks under static compression is presented. Components of the stress-strain state of the thin-layer elements were investigated, and rate of the thin rubber layer compression under the action of vertically applied force was calculated. In numerical calculation, weak compressibility of rubber was simulated by moment force of the finite element for weakly compressible materials, which assumes triple approximation of displacement fields, deformation components, and volume change function. The numerical solution was obtained by the finite element method for different radius-thickness ratios in case of geometrically nonlinear elastic and viscoelastic deformation.