Abstract: Small-diameter vitreous cylinders, for example glass tubes, are maintained under lateral (radial) compression and are precision rolled through grinding wheels, thus fully separating the cylinders into as many cylindrical components as desired. The rolling is effected by maintaining several glass cylinders in laterally-adjacent relationship between a drive roller and a pressure sheet, the latter being under very substantial tension. Thin grinder wheels extend through slots in the pressure sheet and thereby grind completely through the rolling cylinders. The drive roller and pressure sheet continue to roll the substantially separated cylinders, in precise synchronism, so that there is no breaking but instead only grinding.