The three-dimensional mathematical model of temperature and thermal stress field of the blast furnace stave is built. The radiation heat transmitted from solid materials (coke and ore) to inner surface of the stave, which has been neglected by other studies, is taken into account. The cast steel stave is studied and the finite element method is used to perform the computational analysis with soft ANSYS. Numerical calculations show very good agreement with the results of experiment. Heat transfer analysis is made of the effect of the cooling water velocity and temperature, the cooling channel inter-distance and diameter, the lining material, the cooling water scale, the coating layer on the external surface of the cooling water pipe as well as the gas clearance on the maximum temperature and thermal stress of the stave hot surface. It is found that reducing the water temperature and increasing the water velocity would be uneconomical. The heat transfer and hence the maximum temperature and thermal stress in the stave can be controlled by property adjusting operating conditions of the blast furnace, such as the gas flow, cooling channel inter-distance and diameter, lining material, coating layer and gas clearance. (c) 2007 Elsevier Ltd. All rights reserved.