Abstract: The present invention relates to a process for riveting materials by means of a blind rivet and corresponding blind rivets. The process of the invention in particular carries out the step of stretching the body of the sleeve (31) before blocking it from one part to another of an assemblage (13, 14) between an abutment head (50) and a blocking head (51). The extending of the body of the sleeve is especially permitted by the cooperation of a stop means (44) with a shoulder (36a) of the shank of the mandrel (32), and by the pulling exerted on the mandrel. The present invention also relates to blind rivets adapted to be set by the process of the invention.