In a known method for producing a tube of quartz glass by elongation, a hollow cylinder of quartz glass is continuously supplied to a heating zone, softened therein zone by zone, and a tube strand is drawn in the direction of a drawing axis out of the softened region by using a roll puller, the roll puller comprising a frame by which a plurality of puller rolls are fixed, which are rotatable around a rotation axis and which are distributed over the circumference of the tube strand and adjoining the tube strand with their cylindrical outer surface. Starting therefrom, to indicate a vertical drawing method in which a high draw ratio can also be accomplished with little constructional effort by using a take-off unit in the form of a roll puller and which simultaneously allows an optimization of the dimensional stability of the quartz glass tubes obtained, and which particularly avoids material losses caused by ovality and siding, the invention suggests that the frame of the roll puller s stationary, and the hollow cylinder and the tube strand are rotated about the drawing axis relative to one another, the relative rotation being set to a range between 0.01 and 5 revolutions per linear meter of drawn-off tube strand.