Abstract: A headless rivet is disclosed as made from steel or suitable material that provides superior compressive strength compared to conventional rivets and to that of a material to be riveted together and of a height or axial thickness equal to the sum of the materials to be riveted, the rivet having flat end surfaces and a shoulder interposed therebetween with curved neck portions extending from said shoulder to said flat ends. The curved neck portions have a predetermined radius and a predetermined depth of concavity determined according to the height of the rivet. Another embodiment discloses a rivet having ridges interposed between the shoulder and the flat ends including respective neck portions extending from said shoulder to said ridges to said flat ends.