In the manufacture of cylindrical, seam-welded tube from strip stock wherein a strip is cold rolled into a cylindrical tube and the longitudinal edges of the strip are welded along a longitudinal seam of the tube, the weld operation leaving a longitudinal, raised bead on the internal cylindrical surface of the tube, a procedure for removing the weld bead including the steps of distending the internal surface of the tube in a plane containing the weld bead to a predetermined dimension exceeding the nominal internal diameter of the welded tube thereby to locate the bead at a constant radial distance from the longitudinal axis of the tube, disposing within the tube a cutting tool having a cutting edge located at a fixed radial distance from the axis of the tube exceeding the constant radial distance, and effecting relative longitudinal movement between the cutting tool and the tube so that the weld bead is removed to a constant depth.