Abstract: According to the linear thermoelasticity and the mechanical characteristics of blast furnace hearth due to thermal expansion, the formulae to calculate the stress and deformation of BF hearth are deduced under the conditions that 2-D temperature distribution is axisymmetric and the pressure distribution is uniform. Analyzing the stress of BF hearth in overheating state and that of furnace lining before and after reinforcing the longitudinally cracked furnace shell, the lining strength resulting from the control of its outside tensile strength is obtained. Then, the minimum interface pressure meeting the strength requirement is derived from the outside surface strength of furnace lining, thus providing the conceptual design for reinforcing the longitudinally cracked furnace shell with a criterion for the reinforcement. A numerical example is given as reference for relevant calculation.