Constructively nonlinear problems with unilateral constraints and friction with unknown in advance contact zone are frequent in the calculation of various structures. Nowadays the numerical solution of contact problems is being realized usually on the basis of different schemes of finite-element method. A computational model of contact of elastic systems with using the contact finite elements in form of plane frame or space frame is proposed. The numerical method, based on the discrete model and step-by-step schemes, allows the analysis of contact interaction in problems of structural mechanics and has advantages when the problem decision depends on character and history of the loading facilities. The problems of structures and buildings analysis with unilateral constraints and friction both for static and dynamic loads are considered and taking into account the complicated conditions of contact and other factors, which approximate the design scheme to the real structure conditions.