This article describes the joining of thin metal sheets by a single stroke clinching process. Elastic-plastic and rigid-plastic finite element analysis were applied by employing Coulomb friction and constant shear friction in order to investigate the behavior of the clinch joint formation process. Four process variables, such as die diameter, die depth, groove width, and groove corner radius were selected to investigate the parametric effect on the clinch joint. The strength of clinch joints were evaluated by examining the separation strengths, such as peel strength and tensile shear strength, respectively. A failure diagram was constructed that summarizes the analysis results. The simulation results showed that die diameter and depth were the most decisive parameters for controlling the quality of the clinch joint, while the bottom's thickness was the most important evaluation parameter to determine the separation strengths.