In a known method for producing tubes of quartz glass, a hollow cylinder (2) of quartz glass is continuously supplied to a heating zone (1) and is softened therein in regions, and a tube strand (21) is drawn off at a drawing speed from the softened region with formation of a drawing bulb (26), and the tubes to be produced are cut to length in the form of tube strand pieces by separating the tube strand (21) at a desired separation point (T, Vu, Vo) and an internal pressure differing from the external pressure applied to the outer cladding is maintained in the inner bore (4) of the hollow cylinder (2) in that the inner bore (4) of the tube strand is provided with a flow obstacle. Starting therefrom to indicate a simple method which permits the manufacture of particularly large volume quartz glass tubes with utmost precision, while observing narrow tolerances, it is suggested according to the invention that the flow obstacle should be configured as a constriction (28, 29) of the inner bore which is produced by softening and plastic deformation of the tube strand in the area of a deformation zone (Vu, Vo).