In this paper, a finite element approach to simulating a self-piercing riveting process is presented. The detailed formulation and numerical scheme are introduced. The material-material contact interface is formulated by a penalty method. A complicated self-piercing riveting process, which is not actual but only for the purpose of test of the approach, is simulated and the predictions are shown with emphasis on the variation of finite elements especially around the tip of the rivet of which shape is of great importance for solution accuracy.