Residual stresses, which can be produced during the welding process, play an important role in an industrial field. Welding residual stresses are exerting negative effect on the fatigue behavior and integrity of structure. In this study, as a result of the thermal elasto-plastic finite element analysis for the welds of a nuclear component, the residual stress distributions are estimated for as-welded condition. Also, finite element techniques are developed to simulate the relaxation of the residual stresses according to the various mechanical stress relieving(MSR) loads such as hydrostatic pressure loading, tensile pipe-end loading, and mechanical stress improvement process(MSIP) loading. Finally, the results of residual stress redistributions for various loading conditions are compared and reviewed qualitatively and quantitatively to find an optimum loading condition.