A thick-walled SUS316 saddle tube-pipe welded joint is used in nuclear power equipment. A very long computing time and huge memory space are needed to simulate welding residual stress when the thermo-elastic-plastic finite element method is used because of the complex shapes, large sizes, and many weld passes of this joint. To solve the computational problem, two efficient and accurate computational approaches were proposed based on MSC. Marc finite element software platform. In the first computational approach, the finite element model of the SUS316 saddle tube-pipe welded joint was established with the same dimensions as the actual joint. Two heat sources were used to balance the computing time and calculation precision. The moving heat-source model was used to simulate the heat input for the backing and cover passes. In contrast, the instantaneous heat-source model was employed to consider the heat input for the other passes. Considering the geometric symmetry, a quarter model was developed in the second computational approach, and the instantaneous heat-source model was used to model the heat input for all passes. In the material model, both work hardening isotropic rule and annealing effect were considered because SUS316 is sensitive to work hardening. The simulation results of the thermal cycle during the welding process and residual stress distribution in and near the fusion zone were compared using the measured data. The results of thermal cycles and the residual stress distributions obtained using two computational approaches matched the experimental measurements. When the first computational approach was used, not only the residual stress distribution in the whole welded joints could be obtained, but also the features of residual stress distribution near the weld start-end location were able to capture. The second computational approach could predict the magnitude and distribution of residual stress in the stable range of the joint and could save computing time and huge memory space. Thus, the second computational approach is useful for practical engineering applications.