Residual stresses are inherently self-balanced stresses that arise due to non-uniform development of Eigen strains during processes like welding. Tensile residual stress in weld joints have a detrimental effect on the structural integrity and life of an engineering component, Accurate estimation and minimization of residual stress is a pre-requisite to qualify a component for durable service in severe environments e.g. in nuclear power plants. Dissimilar weld joints are fabricated to provide the structural and functional continuity whenever equipment in a process line is fabricated. A typical and relevant example is the weld joint between Modified 9Cr-1Mo steel (P91) and AISI type stainless steel 304 which finds application in nuclear power plants and process industries. Computer aided numerical simulation provide detailed information of the magnitude and distribution of residual stress in the component. This paper describes a numerical study carried out for evaluation of residual stress occurring in dissimilar butt weld joints between P91 and SS304 plates and circumferentially welded pipes. This covers sequential coupled thermo-metallurgical and mechanical FEM time-step analysis using three-dimensional models. The model predicted residual stresses are compared with residual stresses in weld joints of P91 and SS304.