The recent development of the finite element method has been giving a favor to analysis of complex subjects in structural engineering. In this paper, the method is applied to analyze the stress and strain history during welding as the thermo-elasto-plastic problem of bilinear strain hardening orthotropic plate. Though the plate has not only in-plane but also out-of-plane rigidities, the latter is neglected in this study because of the secondary importance in most welding problems. The approach in this problem is based on the Mises yield criterion and the Prandtl-Reuss flow rule in conjunction with anisotropic parameters of elasticity and plasticity. As a basic example of the application, the history of deformations and stresses under welding are analyzed in case of a rectangular plate. The results indicate qualitatively the usefulness of the method.