A flame cutting apparatus is disclosed which has been particularly configured for coping the end portion of a structural steel I-beam workpiece. The apparatus includes a roller conveyor for receiving the workpiece, and a frame positioned in association with the conveyor. A first carriage is provided which is movable along the frame in a direction parallel to the longitudinal axis of the workpiece. A pair of second carriages are provided on the first carriage, and are movable therewith, with the second carriages further being movable relative to each other in a horizontal direction transverse to the workpiece. Each of the second carriages is provided with a pair of flame cutting torches, with arrangements provided for further moving the torches vertically with respect to the workpiece. Associated automatic controls operate the apparatus such that movement of the cutting torches along three axes is effected for coping the workpiece.