Abstract: A method and apparatus are disclosed for shaping an end of a tube in a configuration such that it may be joined to the surface of another body as by welding. The method disclosed involves profiling the end of a tube to conform to the surface of a body to which the tube end is to be joined, with a notional line on the end face that corresponds to the theoretical line of contact of the tube and body, cutting the tube wall at the profiled end to provide a beveled surface over the face of the end to the outer peripheral surface of the tube, and controlling the cutting so that the bevel surface formed progresses inwardly through the tube wall thickness to form a transition line on the profiled end face that substantially follows the notional line of contact between the innermost and the outermost peripheral edges of the profiled end face.