The structure of cooling stave was simplified with equivalent convective heat transfer coefficient, and the thermal stress axisymmetric calculation model of blast furnace hearth linings under erosion state was established. The thermal stresses of familiar erosion states were analyzed. The thermal stress concentration of erosion part is an importance cause of erosion development. ‘Elephant-foot’ erosion seldom develops to ‘boiler-bottom’ erosion. ‘Boiler-bottom’ erosion is a ideal long life erosion state. When the erosion stabilizes, smaller cooling intensity is favorable to linings stabilization.