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This article describes a mathematical model to predict the temperature, thermal deformation and stress in a copper stave with no accretion layer during operation. The effects of gas temperature, cooling water velocity, copper stave thickness and bolt position on temperature, thermal deformation and stress of copper stave are investigated. The results show that a maximum temperature, about 422.5 K (149.5 °C), is found just near the top or bottom of the copper stave hot face. Copper stave deforms into the typical parabolic arc. Decreasing gas temperature can decrease the temperature, thermal deformation and stress, and decreasing the distance between the bolts and top or bottom border of copper stave are available in decreasing the copper stave thermal deformation, therefore improving the copper stave life. Increasing copper stave thickness can increase the temperature and thermal deformation for smaller copper stave thickness, while the thermal deformation in copper stave decreases with copper stave thickness increase for higher copper stave thickness. Water velocity has little effect on temperature and thermal deformation in copper stave, while much effect on the thermal stress around the root of the pipe. [ABSTRACT FROM AUTHOR]