An analysis of the development of the finite element method in the USSR is given. Vibrations of plates and shells, as well as structures located on an elastic base are considered in detail. For rod systems, solutions to the problem of oscillations of arches and beams during the transition beyond the elastic limit are given and the process of destruction during oscillations is studied. These nonlinear problems have been reduced to numerical results using the finite element method. They also received coverage of the optimization problem, the use of risk theory and the problem of stress control theory.