The main structural material used in the building of Fast Breeder Reactors (FBR) is stainless steel of type 316L(N). Finite Element Model (FEM)-based simulations were carried out to understand the effect of various welding processes on the residual stresses induced in 316L(N) stainless steel primary sodium-carrying pipes with an inner diameter of 208 mm and a wall thickness of 5.6 mm. The welding processes considered include multi-pass Tungsten Inert Gas (TIG) welding, A-TIG, laser, hybrid laser-TIG, and Hybrid laser-Metal Inert Gas (MIG). First, single or hybrid heat sources are chosen based on the welding process, and then weld bead profiles obtained during simulation are made to match with that of the actual weld bead profiles obtained during experiments. Then, the optimised heat source is employed for the thermal analysis. The thermal analysis output is then successively linked and provided as input to the mechanical analysis, which uses an isotropic hardening model to predict hoop and axial residual stresses in pipe weld joints. The results show that the A-TIG weld joint exhibited lower hoop stress (165 MPa at inner diameter and -2 MPa at outer diameter) in comparison with that of the other weld joints. The lower residual stress is attributed due to the straight-sided weld bead, lower peak temperature, and slower cooling rate of the A-TIG welding. Therefore, A-TIG welding is recommended among the chosen fusion welding processes for welding of 316L(N) stainless steel primary sodium carrying pipes to minimise the residual stresses and mitigate the premature failure of the pipe weld joints.