A self-clinching fastener for attachment to a plastically deformable metal substrate, the self-clinching fastener comprising: a body portion with a central axis, the body portion including an outer peripheral surface extending in a direction of the central axis, and an annular-shaped surface extending in a direction perpendicular to the central axis; a punch portion being coaxial with the central axis and extending from the body portion such that the annular-shaped surface encircles the punch portion, the punch portion including an outer peripheral surface extending in the direction of the central axis, the outer peripheral surface of the punch portion having a cylindrical profile that resides on an imaginary circumferential plane; and a plurality of spaced apart lugs encircling the punch portion and axially projecting outwards from the annular-shaped surface, one of the lugs including a contact face configured to engage said metal substrate, the contact face declining, relative to an imaginary horizontal plane on which the annular-shaped surface lies, in a radially outwards direction of the self-clinching fastener, wherein the outer peripheral surface of the punch portion includes a plurality of spaced apart cutouts encircling the punch portion, each of the plurality of spaced apart cutouts being recessed with respect to the imaginary circumferential plane and including a cutout surface that is concave, and wherein the contact face has a first end portion and a second end portion, the first end portion being formed with the cutout surface of a corresponding cutout of the plurality of spaced apart cutouts, and the second end portion being positioned radially outwards therefrom, and wherein the contact face continuously declines from the first end portion to the second end portion. a body portion with a central axis, the body portion including an outer peripheral surface extending in a direction of the central axis, and an annular-shaped surface extending in a direction perpendicular to the central axis; a punch portion being coaxial with the central axis and extending from the body portion such that the annular-shaped surface encircles the punch portion, the punch portion including an outer peripheral surface extending in the direction of the central axis, the outer peripheral surface of the punch portion having a cylindrical profile that resides on an imaginary circumferential plane; and a plurality of spaced apart lugs encircling the punch portion and axially projecting outwards from the annular-shaped surface, one of the lugs including a contact face configured to engage said metal substrate, the contact face declining, relative to an imaginary horizontal plane on which the annular-shaped surface lies, in a radially outwards direction of the self-clinching fastener, wherein the outer peripheral surface of the punch portion includes a plurality of spaced apart cutouts encircling the punch portion, each of the plurality of spaced apart cutouts being recessed with respect to the imaginary circumferential plane and including a cutout surface that is concave, and wherein the contact face has a first end portion and a second end portion, the first end portion being formed with the cutout surface of a corresponding cutout of the plurality of spaced apart cutouts, and the second end portion being positioned radially outwards therefrom, and wherein the contact face continuously declines from the first end portion to the second end portion.