In this paper, on the basis of delta-method examined methodology of receipt of dependences "force-settlement" taking into account weak compressibility of elastomeric layer for middle deformations (to 50% - 60%). For this range of deformations supposition is just about the linear resiliency of the deformed elastomeric material. Because a delta-method is on by foot-pace procedure of calculation, then analytical decisions most simply are on delta-method, if for the examined construction already got decisions for small deformations. The use in delta-method of the known linear decisions is simplified by the account of geometrical nonlinearity of change of areas of surface of the deformed elastomeric layer at the calculation of operating on them efforts on the arbitrary stage of loading. At the calculation of stiffness descriptions of delta - method effectively to use the close variation methods of calculation. For illustration of analytical realization of delta - method a prismatic elastomeric shock absorber is considered at axial compression.