Titanium alloy pressure spherical–cylindrical shells enable the effective utilization of the strength of spherical and cylindrical pressure-resistant shell components. In this study, a numerical simulation of the residual stress of a titanium alloy butt-welding plate was conducted by employing sequential coupling and a temperature heat source model. The results of welding residual stress analysis agreed well with the experimental results reported in the literature. Subsequently, the welding residual stress of a titanium alloy pressure spherical–cylindrical shell was calculated and analyzed using the same method. Finally, the influence of residual stress on the ultimate bearing capacity of the shell was assessed. On the inner surface of the shell, the horizontal welding residual tensile stress, perpendicular to the weld path, exhibited a bimodal distribution. The longitudinal welding residual tensile stresses were higher than the horizontal welding residual stress. Near the weld on the outer shell surface, higher longitudinal welding residual tensile stresses existed, whereas the horizontal welding residual stress was compressive. Both the inner and outer shell surfaces exhibited significant longitudinal residual tensile stresses along the weld path, though residual compressive stresses existed on both surfaces. The influence of welding residual stress on the ultimate load-bearing capacity of the shell was minimal.