The thermal expansion of work rolls during hot strip rolling was modeled by a two-dimensional difference method.The calculation model was validated by comparison between the predictions to the measured results.With that model,the effects of rolling process parameters such as the rolling plan,mill pacing,coolant flow rate and stepped cooling on the roll thermal profile were investigated.The result shows that stepped cooling of work rolls can be used to control complicated flatness defects such as quarter buckles during hot strip rolling. The thermal expansion of work rolls during hot strip rolling was modeled by a two-dimensional difference method. The calculation model was validated by comparison between the predictions to the measured results. Where that model, the effects of rolling process parameters such as the rolling plan , mill pacing, coolant flow rate and stepped cooling on the roll thermal profile were investigated. The result shows that stepped cooling of work rolls can be used to control complicated flatness defects such as quarter buckles during hot strip rolling.