The invention starts from a known method for producing a glass body, comprising forming a cylindrical blank by successive deposition of a plurality of material layers on the outer surface of a substrate body which is rotating about its longitudinal axis, by using an arrangement of a plurality of depositors which are directed onto the substrate body and which are fed via supply lines with process media for material layer deposition and which are moved without a reversing movement relative to the longitudinal axis of the substrate body. Starting therefrom, to provide a method for producing a glass body of high homogeneity that can be realized in a constructionally simple way, the invention suggests that the movement of the depositor arrangement along the longitudinal axis of the substrate body should be accompanied by a displacement of the substrate body. An apparatus suited for performing the method is distinguished by a displacement device for a displacement of the soot body which is accompanied by the movement of the depositor arrangement along the longitudinal axis of the substrate body.