A metal rod (20) having a conical or pyramidal cut extremity (20a) is used to make a mandrel for blind rivets. The rod is held in place between a pair of die segments (11) such that its end (26) of a preset length, including the tip protrudes from an upper surface (14) of the segments. Subsequently, a free intermediate portion of the swageable end (26) is axially compressed to form a mandrel head (27) by a punch (12) which has a lower face (17) parallel to the upper surface (14) of the segments with a conical or pyramidal recess (18) formed on the end. The free intermediate portion of the swageable end (26) swells radially outward to form the head (27) having a flat flange (31) from which the tip intrudes. The mandrel, which has the head formed uniformly without any eccentricity about the longitudinal axis of a mandrel body, can be produced inexpensively using a prior art nail manufacturing apparatus.