Aiming at the radiator with tube-to-plate structure applied usually in aeroplane, a two-dimensional model for finite element analysis was established in this work. By ANSYS software, the temperature field and stress field of electron beam brazing (EBB) 1Cr18Ni9Ti stainless steel radiator by two kinds of process were numerically simulated. The calculated results of temperature field show, by the stage-by-stage heating process, the uniform temperature distribution of radiator faying face was obtained. The temperature of most regions is between 1042~1051°C, which is in the range of brazing temperature. The calculation results of stress field indicate, for radial residual stress, the obvious stress concentration region was found in faying face by direct-heating process; while there was no stress concentration in faying face by stage-by-stage heating process. For circumferential residual stress, compared the stage-by-stage heating process with direct-heating process, the peak value of tensile stress reduces by 11.2%. Compared circumferential residual stress with radial residual stress by two kinds of brazing process, the peak value of circumferential tensile stress is higher than radial tensile stress. So the dangerous position of faying face is along circle direction, namely, the heating direction of scanning electron beam. Consequently, the temperature difference between different positions in faying face must be controlled well during heating. The reduction of temperature difference can fall the peak value of tensile stress and improve the distribution of residual stress.