Welding processes cause undesirable problems, such as residual stresses and deformations due to the thermal loads imposed by local heating, melting, and cooling processes. This paper presents a computational modeling technique to simulate the Gas Metal Arc Welding (GMAW) process, emphasizing the effect of the melting bead on the residual stress distribution. Both a three-bar analogy and a three-dimensional thermo-mechanical finite element analysis are carried out in order to explain the effect. Element (de)activation, enthalpy, and adjustment of the reference temperature of thermal strain are considered with respect to the effect of the weld filler metal added to the base metal during a thermo-elastic-plastic analysis. Stress distributions obtained by the present study are compared with measured values and available data from other studies. The effect of the melting bead on the residual stress distribution is discussed and demonstrated.