An elastic?plastic stress mathematical model of hot blast stove shell has been established to investigate the stress distribution and deformation of the shell. The results showed that under the influence of the internal gas pressure, the hot blast stove body shell and main shell occurs bending deformation, squeezes the hot blast manifold and cause stress concentration along the intersection line of hot blast stove body, hot blast main and the hot blast manifold, especially the stove during blast period where plastic deformation occurs around the top and bottom sides of hot blast outlet. Under the influence of tensile stresses along Z-direction around the top and bottom of outlet and compression stress along Y-direction around the right and left side of outlet, the shell near the blast outlet elongates along the horizontal direction and shortens along the vertical direction, the shell near the outlet deforms into an oval. The deformation degree of the hot blast shell near the blast outlet in blast period is much larger than that in combustion period. The repeated deformation of the shell near the outlet between different periods may be harmful to the long campaign life of hot blast stove.