A self-piercing rivet element (10) having a central longitudinal axis (14) with a body part (16) having a larger diameter and with a hollow rivet section (18) of smaller diameter for being pressed into a non-pre-pierced component (60), wherein the rivet section (18) is made to be dilatable at least regionally by means of a die button (20) and tapers in the direction of the central longitudinal axis (14) and away from the body part (16), wherein the hollow rivet section (18) has its largest diameter (D1) in the region of the transition to the body part (16) and the closed peripheral wall with the rivet section (18) reaching its smallest diameter (D3) at its free end (26) and there having a circular opening (24), with the taper of the rivet section (18) having an enclosed angle (α) in the range between 20° and 100°, preferably between 30° and 60° and in particular between 40° and 50°.