Disclosed is a method for the axial building up, in a vertical arrangement, of a hollow cylindrical soot body having no internal support and consisting substantially of silicon dioxide by means of at least one flame hydrolysis build-up burner serving for the soot production. In this method the soot is deposited at the beginning of the build-up onto an auxiliary body, and during the build-up the build-up burner and the growing soot body are rotated relative to one another, and the burner is at the same time held at an unvarying distance from the growing end of the hollow cylinder and centrally above the predetermined cross section of the upwardly growing end of the cylinder wall. The penetration of soot into the interior of the cylinder is prevented by means of a directed gas stream.