This paper presents the deformation of a joined sheet after the clinch riveting process. The DX51D steel sheet with zinc coating was used. The samples to be joined with clinch riveting technology had a thickness of 1 ± 0.05 mm and 1.5 ± 0.1 mm. The sheet deformation was measured before and after the joining process. The rivet was pressed in the sheets with the same dimension between the rivet axis and three sheet edges: 20, 30, and 40 mm. For fixed segments of the die, from the rivet side close to the rivet, the sheet deformation was greater than that of the area with movable segments. The movement of the die’s sliding element caused more sheet material to flow in the space between the fixed part of the die and movable segments. Hence, the sheet deformation in these places was smaller than for the die’s fixed element—the sheet material was less compressed. For sheet thickness values of 1.5 mm and a width value of 20 mm, the bulk of the sheet was observed. For a sheet width of 20 mm, it was observed that the deformation of the upper and lower sheets in the area of the rivet was greater than for sheet width values of 30 or 40 mm.