A support shoe for supporting an abrasive tape having an abrasive face and an opposed back face, wherein the support shoe comprises a pressure face including a frictional engagement material for frictionally engaging the back face of the abrasive tape. The frictional engagement material comprises a plurality of cells and a first frictional engagement surface comprising a plurality of particles distributed and arranged within the plurality of cells, wherein at least some of the plurality of particles are fixed within and extend from the plurality of cells, so that when the back face of the abrasive tape contacts the first frictional engagement surface, the plurality of particles attenuate relative movement between the abrasive tape and the pressure face in response to shear forces induced during abrading. The pressure face may be curvilinear, arcuate, convex, or concave. The frictional engagement material may be attached to the pressure face by brazing, sintering, adhering, or soldering. The back face of the abrasive tape may include a second frictional engagement surface, so that when the second frictional engagement surface contacts the first frictional engagement surface, the plurality of particles attenuate relative movement between the abrasive tape and the pressure face in response to shear forces induced during abrading. The frictional engagement material may further comprise a matrix material in the cells for holding the plurality of particles within the cells, wherein this matrix material may comprise a sintered matrix material.