The forming mechanism of clinch joints, for various materials arrangement, using a punch and a rigid die, is well known. The basic technological parameter of the process is the parameter X – the minimal thickness of the embossment. Usually, the lower the X parameter, the greater the joint interlock. This paper presents the possibility of forming a pressed joint for two 1.5 [mm] thick sheets made of HX340 steel. The joint was formed using an additional deformable steel rivet with a hardness of 400HV1. Different values of rivet pressing below the initial surface of the upper sheet were chosen: 0, 0.15, 0.30, 0.45 and 0.60 (in [mm]). The punch positioning accuracy was 0.01 [mm]. For the mentioned rivet pressing distances, forming tests were performed using an ‘‘SKB’’ die with three die depths: 1.45, 1.60 and 1.75 (in [mm]). Observations and measurements of the characteristic geometric dimensions of the interlock were made. Furthermore, the strength of the clinch-riveted joints was analysed. The greater the rivet pressing distance, the larger the interlock parameters. Furthermore, depending on the size of the rivet pressing distance, different failure mechanisms of the lap joint were observed in the tensile shear tests.