The problems of protecting equipment, structures and operators from the harmful effects of vibrations are among the most painful topics of modern mechanical engineering. In this research an original design of a friction shock absorber is presented in which the principle of operation is based on the contact interaction of a package of open shells with weakly compressible deformable filler. The proposed design is simple and technologically advanced, suitable for operation under high dynamic loads and at the same time has a compact transverse dimension. Such shock absorbers are projected to be used in the mining and oil and gas industries. A finite element model of a friction shock absorber with two contact pairs has been constructed: the first contact pair is "filler - package of open shells"; the second contact pair is "inner shell of the package - outer shell". The contacting bodies were presented as separate arrays of finite elements and the conditions of frictional interaction on the contact surfaces were set in the form of Coulomb's law. We considered the behavior of such a structurally nonlinear system under the action of a monotonic and nonmonotonic load. In the course of the study, the main operational characteristics of the shock absorber including the strength, rigidity, hysteresis characteristics and natural frequencies were determined. The possibility of adjusting the rigidity and shock-absorbing characteristics of the proposed device is discussed.