The wall of a pressure vessel tube having cracks or other discontinuities is repaired by localized melting with the addition of an alloying material. The melting reforms or eliminates the discontinuity while the alloying material improves the physical and chemical properties of the reformed tube wall. The alloying material may be added as an insert or as a weld wire. The insert may be melted in only its center section to ensure that the entire weld is properly alloyed. Sections of the insert which are not melted may be expanded to be in intimate contact with the tube. The weld wire feed means may be integral with the welding head. A post-weld stress relief process may be applied to the welded area to reduce residual stress generated by the welding operation.