A flexible abrasive (10) with a preset shape corresponding to the shape of the operating head of a machine tool such as a sanding machine and comprising a first support (16) made from a woven or non-woven material where a lower surface can be fixed to a backing plate or a pad of the operating head. The abrasive surface is made from at least two strips (20-23) applied side by side and parallel to each other and where the second support (11) of each strip (20-23) is separately fixed on the first support (16), and where the abrasive surface (18) is shaped so that it can be applied to the backing plate or pad of the operating head.