Resistance butt welding (RBW) is the main process used by AREVA to weld end plugs to fuel rod cladding. The combination of current, electrical resistivity of the plug–cladding contact, and applied pressure is set so as to weld the parts without fusion of the materials. Because this is a solid state welding process, one of its main advantages is that the corrosion behavior of the welds is very good, because it is not affected by any potential contamination from the welding atmosphere or other components. The RBW welds are geometrically characterized by plastic deformation of the welded interface that depends on process parameters such as applied current and pressure, welding time, and initial geometry of the parts. Microstructural evolutions and extension of the heat-affected zones are also consequences of these parameters. In order to better understand the multiphysical phenomena involved during the very short welding time of this process, numerical modeling of RBW was developed. The model is also very useful for investigating new configurations and further optimizing weld quality with a reduced number of welding samples. The RBW numerical model was implemented within the finite element code FORGE, and electrical phenomena were coupled with thermal and mechanical ones. Mechanical properties of the tube and the plug were described as a function of strain, strain rate, and temperature. The temperature and pressure dependence of the electrical contact resistance were also determined and taken into account. Thanks to a good description of the thermal and mechanical history of the weld, numerical results, such as weld geometry, plastic strain, and heat-affected zones, were in good agreement with experimental ones. The model was primarily used to understand the effects of process parameters on geometry and temperature, but it was also used to optimize welding conditions.