A self-punching press-fit element, in particular a punching nut, has a head part with a head bearing for bearing on a component, as well as a punching collar having an end-side cutting edge. An undercut is configured between the punching collar and the head bearing. An encircling displacement web is configured so as to adjoin the punching collar on the head bearing, the encircling displacement web being adjoined in the radial direction by a further external region of the head bearing. The further external region in the longitudinal direction is set back in relation to the displacement web. During the configuration of the press-fit connection, material is press-fitted from the upper side of the component into the undercut by the displacement web. A deformation of the lower side of the component is preferably not performed.