Calculates the main characteristics of a novel shock (energy) absorber: load-displacement diagram, maximum stresses and absorption energy for the cycle of loading. The shock absorber contains spring and thin elastic reversing shell of revolution with nonlinear behavior. The methodology of calculation is based on the application of new asymptotic formulae, obtained for the Reissnerís equations describing axially symmetric deformation of the orthotropic thin shells of revolution by large deflections. The accuracy of the asymptotic formulae corresponds to the accuracy of the initial equations of thin shell theory.