A numerical investigation is provided to study the residual stress states in multi-pass TIG welding of stainless steel SUS304 pipe. An uncoupled thermomechanical three-dimensional finite element model is developed using the ABAQUS software for a circular weld design around the pipe. The effects of weld pass numbers, electrode moving speed, and heat input on the internal and external surface tensions of the pipe are investigated. The simulation results show that by increasing the welding speed, the axial tensile stresses decrease on the pipe surfaces. In the case of hoop stress, as the welding speed raises, the tensile and compressive stresses are increased for both two- and three-pass welding. However, the width of the stress zone becomes narrower in higher welding speeds. The hoop stresses, in comparison with the axial stresses, are more strongly influenced by the welding speed and the heat input. Furthermore, using the three-pass welding process results in much lower stresses in comparison with the two-pass one.