A glass composition to be softened is fed to a heating zone and is shaped continuously into a cylindrical component in a deformation zone, and the cross-sectional geometry of the component is determined. A feed device, a heating device, and a take-off device are provided, and a glass composition is supplied continuously by the feed device to the heating device, where it is softened, the component being formed from the softened glass composition by means of the take-off device under formation of a deformation zone. To produce a component with only slight deviations from the desired cross-sectional geometry and to provide a flexible apparatus suitable for this purpose, the glass composition is locally heated or cooled in at least one deformation area, which extends over only a part of the circumference of the deformation zone, as a function of a determined deviation of the cross-sectional geometry from a nominal geometry. Heating or cooling are provided, which act locally on at least one deformation area, which extends over only a part of the circumference of the deformation zone.