Steel bridges, which have been damaged by load and corrosion, need repair or strengthening. That is a cause of decreasing the durability of structure. In order to solve these problems, welding repair and strengthening methods can be considered. In general, cutting and welding procedure is carried out during the repair welding. Therefore, the investigation of the behavior of residual stress and deformation generated by cutting and welding is very important for safety of structure. Residual stress and deformation produced by gas cutting and arc welding were analyzed using 2D and 3D thermal elasto-plastic FEM. According to the results, the magnitude of temperature was analyzed by 2D-FEM is smaller than that was analyzed using the 3D-FEM at the start and end edge of flange. And the magnitude and distribution of residual stress of perpendicular direction of the cutting line and welding line was analyzed by the 2D-FEM was similar to that was analyzed by 3D-FEM. Therefore, it is possible to predict cutting and welding residual stress by 2D and 3D FEM.