A flexible honeycomb panel containing wire or other abrasive material for abrading a workpiece, including a honeycomb core embedded with a quantity of abrasive material, and a facing sheet. The honeycomb core is formed of undulating strips of resilient thermoplastic material that are thermal compression bonded together to form cell walls defining a plurality of contiguous regularly shaped cells. The abrasive material is contained within the strips. The facing sheet, formed of resilient thermoplastic material, is thermal compression bonded to a face of the core. The bonding is accomplished by simultaneously applying heat and pressure to the joinder of the facing sheet and the core. The opposite face of the core remains uncovered. In use, the uncovered face of the core is brought into rubbing contact with the workpiece. The force imparted by the frictional contact is sufficient to wear down the plastic cell wall material, expose the abrasive material, and cause the material to come into contact with the workpiece with sufficient force to abrade the surface of the workpiece.