PURPOSE: To stabilize the traveling direction of a beveling machine with a simple means by making the roll which is further from the end face of a work freely rollable among the plural rolls which roll along the front and rear surfaces on the end face of the work.

CONSTITUTION: A beveling machine is set on the end face of a work 10 and is pressed by a pressurizing means 9 to grasp the work 10 among rolls 3, 8, 4, then the roll 3 is driven to rotate by a motor 5 by which the beveling machine is self-run along the end face of the work 10 and the end face of the work 10 is beveled by a melt cutting device 2. The rolls 3, 8, 4 held in contact with the work 10 by the means 9 are positioned axially at right angles to the end face of the work 10. All the rolls 4, 8 are freely rollable idle rolls. The beveling machine is thus regulated in its running and is run stably, whereby a uniformly beveled edge is formed.