The paper presents the model of the tests on joints obtained by clinching (mechanical joining) high-strength TRIP690 steels. A numerical finite element analysis of the joint with a bottom thickness of 0.6, 0.7 and 0.8 mm was carried out using the MSC.MARC&MENTAT implicit software. Similarly as in the physical tests, numerical analysis predicted that the joint can carry a greater normal force when the thickness of the bottom is reduced. The model can be used in further studies aimed at determining the optimum shape and strength of such joints. In the literature, two basic modes of failure are distinguished. The first is associated with insufficient material deformation, whereas the second, with the lack of material in the joint’s neck due to, for example, excessive displacement of the tools. For TRIP690 steel the only first mode of failure was observed.