A method for forming a hollow cylinder, in a single step or in as small a number of steps as possible, into a quartz glass tube with a large outer diameter and high dimensional stability is provided. The cylinder, while rotating about a rotation axis, is softened in portions in a heating zone which is moved at a relative feed rate Va, and the softened portion is radially expanded by a centrifugal force and/or an internal overpressure applied in the hollow cylinder bore so as to form a deformation zone. The tube is continuously shaped with an outer diameter D2 which is greater than that of the hollow cylinder D1. The radial expansion of the softened portion is carried out at a location-dependent radial expansion rate Vr, the profile of which along the deformation zone has a maximum value Vr,max which is smaller than two times the feed rate Va.