Abstract: A diamond-set wire for cutting stony materials or the like, comprises a cable (5; 25) to which a series of abrasive units (3; 23) is connected. Each abrasive unit (3; 23) includes a cutting member (7; 27) which has at least one portion made of abrasive material (9; 29) disposed radially on the outside of the cable (5; 25), the portions of the cutting members (7; 27) made of abrasive material (9; 29) being spaced apart along the cable (5; 25). Each abrasive unit (3; 23) is anchored to the cable (5; 25) by means of a plastics or elastomeric filling material (18; 38) interposed between the unit and the cable (5; 25). The adjacent abrasive units (3; 23) are arranged in contact with one another.