Elastomeric shock absorbers are used in various technical fields to protect equipment from impacts. Elastomers made in an arched shape have complex nonlinear force characteristics due to large deformations, loss of stability of working elements and closing of surfaces. In this regard, obtaining the power characteristics of arched elastomeric shock absorbers is a complex computational problem. It is noteworthy that, in the literature, these characteristics are given only for the case of normal compression. However, when assessing the possibility of using a shock-absorbing system based on arched elastomeric shock absorbers, it is necessary to take into account their lateral force. The study proposes to solve the problem of determining the elastic force characteristics of a shock absorber while operating in the normal and lateral directions in the system of finite element analysis in a flat formulation. Analytical expressions are obtained for the normal and transverse static reactions of the shock absorber under simultaneous loading in the normal and transverse directions. Analytic expressions can be used to simulate complex shock-absorbing systems with a large number of such shock absorbers.