In the design of Vibration isolator it is often necessary to ensure a reduction (or increase) of the value of frequency ηr, that requires the ability to calculate the stiffness characteristics of elastomeric Vibration isolator in the low finite and medium finite deformations. A similar problem arises in the design and calculation of equifrequent rubber-metal compensating devices, which find application in various fields of engineering and construction industries, effectively replacing the hydro- pneumatic - spring compensating devices, working under axial stress-strain. In this case, the stiffness characteristic of “force – settlement” P = P (Δ), even for small finite deformations, will be non-linear (or piecewise linear). In this title proposed a method for determination of rigidity dependence "Force - Settlement" for shock-absorbing elements with absolutely rigid moving (parallel to the vertical axis z) vertical side stops being under pressure, and it is taken into account low compressibility of material of rubber layers. Received solutions can be used to find the dependence „force - settlement” of cylindrical shock absorbers, as well as in projecting such shock absorbers.