Abstract: A flame-cutting apparatus comprising a burner guided for movement around a rotating pipe to travel along a curved path along the surface of the pipe corresponding to the line of intersection of two pipes. The burner is pivotably supported on a guide for movement about an axis perpendicular to the axis of the jet flame of the burner. A template corresponding to a chamfer to be produced in the surface of the element being cut by the jet flame includes two parts, one being pivotable with respect to the other about an axis common to both parts. A scanner rotates at an angular velocity corresponding to the angular velocity of rotation of the pipe being cut and the template is resiliently urged against the scanner to be axially displaced thereby and to transmit such displacement through a mechanism to effect pivotal movement of the burner to produce the desired chamfer of the cut edge of the pipe.