The clinching joining of three steel sheets (DC06, DX53D, and H220PD type) was studied by utilization of the finite element method. Clinched joints were also prepared experimentally by joining the above-mentioned steels with the thickness of 0.8 mm (DC06 and DX53D) and 1.0 mm (H220PD). The experimental tool works as single stroke tool, while prepared joints have circular axisymmetric shape, and the rigid die has no flexible segments. Finite element calculations were carried out in ANSYS software under simplified-axisymmetric conditions. Metallographic sections were also prepared from experimentally developed joints to make possible to directly compare the results of simulated and experimental approach. The results of computational approach are discussed and compared to the experimental ones.