It is well known that during welding or cutting, transient thermal stresses and strains are produced in steel structures and these residual stresses could be one of the causes of cold cracking in cooporation with diffusion of hydrogen and restraint rigidity of the structures. In this paper, a new calculation technique of residual stresses and strains due to welding is described. Thermal elastic-plastic stress analysis for one-dimensional problems has been studied for many years. In the previous paper, the authors reported the formulation of the finite element technique based on displacement method which could be applied to two or three dimensional thermal elastic-plastic stress problems. Recently, more complicated and realistic problems could be solved by using powerful numerical methods such as finite element technique, etc., because of the remarkable progress in computer application. On the contrary, the authors present a new calculation method which combines the idea of dividing the whole region into finite elements such as F. E. M. with the modified initial strain method and stress function introduced by Fujimoto. The above-mentioned stress function corresponds to the concept of the influence function studied by Kawai, and since this influence method is a sort of stress method, it is easily understood that the results calculated by this new method could show fair coincidence with the experimental data. It is comfirmed that thermal elastic-plastic stress analysis based on inherent strain method is rather effective compared with the finite element method of displacement type, when more accurate stress distribution is required, and also that calculation time would be much less when many incremental repetitions are needed.