Thermal stress of SEN was analyzed by using finite element method (FEM). The results disclose: (1) for the tapered zone of SEN, the thermal stress reaches its peak after casting for about 30 s, at this moment, the axial stress is the largest, the circumferential stress comes the second and the radial stress is the smallest; (2) when SEN suffers the thermal stress, the inner wall suffers the pressure stress, and the shorter the distance from the inner wall is, the larger the pressure stress is; the outer wall suffers the tensile stress, and the shorter the distance from the outer wall is, the larger the tensile stress is; the axial stress holds a dominant position in the tapered zone, while the circumferential stress takes the lead in the cylindrical zone; (3) as angle α of SEN’s tapered zone increases, the thermal stress grows obviously when α is larger than 110°; while the thermal stress reduces obviously, when α is larger than 140°; thus, for SEN design, it is essential to avoid the interval of α=110°-140°.