A method for welding tubes in a shell and tube heat exchanger, including forming ring-shaped tube sheet grooves on the tube sheet at the shell side, inserting tube joint members into the tube insertion holes of the tube sheet, producing ring wires by cutting a welding wire into pieces and bending the pieces into a ring shape, affixing the ring wire to the outer circumference of one end of the tube, inserting the end of the tube into the tube sheet such that the end of the tube contacts one end of the tube joint member and is located within the recessed distance range of the tube sheet groove, and performing shell side welding by inserting a welding torch into the tube joint member and welding the end of the tube joint member, the end of the tube and the joint part to the tube sheet at the shell side using the ring wire as filler metal.