The high energy intensity of industry and the importance of natural resources are currently much-discussed topics. Light steel structures made from thin-walled cold-formed (TWCF) profiles play an important role in this discussion because their increased use has significantly reduced the consumption of conventional structural steel. New, more efficient technologies for connections of the TWCF structures, such as punch riveting and clinching, are being developed, which are advantageous in terms of cost and time. An innovative way to obtain the physical properties of a clinch joint and instructions for a detailed reliability assessment of this type of connection is described in this article. The resulting behaviour of the numerical model based on the tensile test of the basic material and suitable boundary conditions was validated by a physical experiment. The computational procedures presented in the article will facilitate the design of steel structures in the field of global static analysis of TWCF light steel structures because the described methods can be generalised and applied in commonly available commercial software. Two variants of the model were prepared and evaluated—with and without slippage in the press jaws. Comparison of the numerical model and experimental results shows compliance.