The distortion and the residual stress are the inevitable consequences of the welding and these may reduce the strength and the quality of the welded structures. To prevent the harmful influence of the welding distortion and the residual stress, their theoretical prediction is necessary. However the existing methods are mostly developed for the study of specimens in laboratories. Compared to the specimens, the structures manufactured in the industry are larger in size and more complex in geometry. For the theoretical prediction applicable to industrial structures, more powerful and practical methods are necessary. To achieve this goal, the authors developed a fast computational method for thermal elastic plastic analysis and an elastic finite element method using inherent deformation.