An anvil for a blind riveting tool for locking the plugs of self-plugging blind rivets. The anvil has a central aperture (11), an annular abutment face (13) peripherally of the aperture (11) and a rim (14) radially inwardly of the abutment face (13) and peripherally of the aperture (11). The rim (14) projects forwardly of the abutment face (13) and has a forward end face (16) which is inclined rearwardly and outwardly and provided with generally concave recesses (15) which extend radially across the end face (16) and divide it into a plurality of lands (20) which during placing of a rivet operate to swage part of the mandrel of the rivet into locking engagement with the shell of the rivet.