Abstract: A method and device are provided for machining transparent glass and vitreous material by means of a single point cutting tool. A portion of the workpiece to be worked is heated integrally and uniformly by a first heat supply, which is spread along the workpiece, to the softening temperature, and simultaneously the surface to be worked is locally heated in the region of the cutting area at the moment of material removal to a depth equal to the cutting depth by a second concentrated heat supply which is superimposed on the first heat supply. All this is provided in such a manner that a turning operation, as well as simultaneously therewith and immediately thereafter a relaxed flow of the work surface, takes place. By means of the method according to the invention, it is possible to turn workpieces of glass and vitreous materials so that the work surface has a high dimensional accuracy, as well as an optical surface quality in particular, such as a smooth and transparent surface.