Abstract: In a laser beam glass cutting method, a glass article to be cut (for example a moulded tumbler having a moil) is maintained at a high temperature below the softening point of the glass and then the glass is repeatedly irradiated with a laser beam along the required cut-off line by rotating the glass. During this step, a tensile force is applied by gravity or by a mechanical device to the part to be cut off. Following removal of the part, the edge of the glass is irradiated again with the laser beam to effect fire-polishing thereof, so as to improve the shape of that edge. During the irradiation by the laser beam, an auxiliary inert gas is blown into the glass article to prevent glass deposition.