Abrasive tools of the disposable type applicable to many types of equipment to sand materials of various types are provided. In particular, the invention relates to devices using rotating abrasive discs for sanding machines, which include a plurality of flexible abrasive discs open at a radial cut and arranged in an overlapping and staggered configuration such as to define an abrasive, lamellar-like work surface with overlapping flaps, wherein each flap is formed of a protruding portion of an abrasive disc. Methods of making such abrasive tools are also provided.