Abstract: A method of riveting comprises inserting a self-piercing rivet into sheet material without full penetration such that the deformed end of the rivet remains encapsulated by an upset annulus of the sheet material. The sheet material is clamped with a substantial force during the riveting operation in the region around the rivet insertion location. The clamping force is maintained constant throughout at least the major part of the riveting operation and has a magnitude of up to 1.5 tonnes. A riveting machine for carrying out the method comprises a punch, means for feeding rivets successively to the punch for insertion into sheet material to be riveted, a die aligned with the punch for deforming the rivet inserted thereby, and clamping means for clamping the sheet material with a substantial force during the riveting operation in the region around the rivet insertion location.