Abstract: A glass vessel edge chamfering method and apparatus wherein heat energy can be controlled readily and chamfering of a glass vessel having a deformed profile, local chamfering and simultaneous processing of the opposite inner and outer sides of a lip of a vessel can be performed readily and besides the efficiency in consumption of energy necessary for chamfering for one glass vessel is improved so that a glass vessel can be processed efficiently in a short time. A pair of positive and negative electrodes are opposed in a predetermined spaced relationship to an edge of a glass vessel, and flame is blown from a pair of burners into gaps between the edge of the glass vessel and the electrodes while a high voltage is applied between the electrodes. Thereupon, electric current flows between the electrodes and the glass vessel by way of the flame and heats the glass vessel by Joule heat when the electric current flows through the glass vessel.