Different grades of austenitic stainless steel and ferritic/martensitic steel are extensively used in different industries, including in nuclear energy generation. These materials are welded using different conventional and advanced welding methods, which invariably introduce residual stresses in the joints. Because of the profound implications of the residual stresses on the in-service performance of welded components, its deeper understanding is necessary for the designers and the manufacturers of the engineering components. Modeling and simulation studies have been performed using finite element based software—SYSWELD, for laser welding of similar metal joints in P91and SS316L, to compute spatial distribution and temporal evolution of residual stresses. The computed results show that the longitudinal component of the residual stress is the most significant in both welded joints. P91 steel shows low a low-tensile/compressive residual stress trough in the fusion zone (FZ) and a high-tensile residual stress peak in the parent metal, adjacent to the heat affected zone (HAZ) on the either side of the joint. On the other-hand, SS316L shows high tensile residual stress peak in the FZ and HAZ. The computed results are presented and discussed in this paper.