Over the past 20-30 years, using the specific properties of rubber (high elasticity, resistance to environmental influences, good dynamic performance, low compressibility, almost linear relationship between stress and strain at strains up to 15% ÷ 20%) developed shock absorbers, possible to realize nonlinear characteristics "force - settlement". The paper proposes a method of calculation of a cylindrical rubber shock absorber cords with hard side stops include of the weak compressibility of rubber. The solution is obtained by the method of Ritsa using the principle of the minimum complete potential energy of deformation. Receiving solutions can be used to find the dependence „force - settlement” cylindrical shock absorbers, as well as in projecting such shock absorbers. When you need to design a shock absorber with a given non-linear stiffness characteristics.