Abstract: A riveting apparatus comprises first and second dies having plane forward end faces for gripping a workpiece over a substantial area round the location to be riveted. The dies have aligned bores which open to said end faces and which are the same as each other in cross section, and a punch and a plunger corresponding to the shape of the bores are slidably mounted in the bores of the first and second dies respectively. A hydraulic piston operates the punch and the forward movement of the punch along the bore of the first die can be terminated by a stop selectively either with the punch and flush with or a predetermined distance short of the end face of the first die. The plunger can be moved hydraulically along its bore toward the punch. In operation of the apparatus, a headless pin is driven through an imperforate workpiece and thereafter each end of the pin is upset while the pin is prevented from moving lengthwise of itself relative to the workpiece.