In a conventional method for the production of an optical component made from quartz glass, a coaxial arrangement with a core rod, surrounded by a quartz glass envelope tube comprising an evacuable inner drilling, is introduced in the vertical direction into a heating zone, softened therein by sections and, with formation of a drawing bulb, elongated to give the quartz glass component. According to the invention, a simple and cheap method based on the above, permitting the production of high-grade optical components by elongation of a coaxial arrangement of core rod and an enveloping tube with great economy, may be achieved, whereby a core rod is used, comprising at least two separate core rods arranged one above the other in the inner drilling and the weight of an upper core rod section is taken by a mounting or support region of the enveloping tube, provided above the drawing bulb.