A shoe for supporting an abrasive tape having an abrasive face and an opposed back face, wherein the shoe comprises a support surface including a frictional engagement material for frictionally engaging the back face of the abrasive tape. The frictional engagement material comprises a plurality of individual frictional engagement areas on a flexible substrate, each frictional engagement area having a plurality of abrasive particles. In an exemplary embodiment, the frictional engagement material comprises diamond abrasive particles retained in a nickel matrix supported on a flexible mesh substrate. The support surface of the shoe may be curvilinear, arcuate, convex, or concave.