The work is devoted to the diagnostics of the stress state of systems that soften the shock load on the vehicle body, the elastic element of the car suspension such as a multi-leaf spring. The construction of a mathematical model taking into account the geometric nonlinearity according to the finite element method theory is considered. Mathematical modelling was carried out to take into account the change in the stiffness matrix of the system when changing its shape. For research, a symmetrical semi-elliptical spring consisting of five leaves is used. All numerous numerical experiments were performed in two computer-aided design (CAD) systems: ANSYS, a heavy multipurpose package and SolidWorks, a middle-level multipurpose package. Computer-aided design algorithms have been developed to expand the capabilities of CAD. The analysis of the results obtained allows to conclude that the traditional models of nonlinearity in ANSYS and SolidWorks give approximately the same results, which at the maximum point differ by 20.6% from the data of a full-scale experiment. When using the proposed model, this difference is reduced to 7.95%.