Steel bridges, which have been damaged by load and corrosion, need repair or strengthening. In general, before the repair welding procedure, cutting procedure carry out. Therefore, the investigating of the behavior of stress generated by cutting is so important for safety of structure. Residual stress produced by gas cutting was 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 program at the start and end edge of flange. And the magnitude and distribution of residual stress of perpendicular to the cutting line was analyzed by the 2D-FEM program was similar to that was analyzed by the 3B-FEM program. Therefore, it is possible to predict of cutting stress by 2D and 3D FEM.