Rolling process to fabricate a strip with even thickness is significant to enhance the quality of the strip. The thickness of a strip can be effectively controlled by pair-cross mills. However, pair-cross mill generates thrust in the axial direction of roller and causes skewness, deflection, twist and even accidental roll chock failure. Therefore, accurate estimation of the thrust of the pair-cross mill during rolling process is necessary to monitor the failure of roll and the quality of products. An empirical equation given by Mitsubishi Heavy Industry (MHI) is hitherto employed, where the thrust is expressed in terms of rolling force, reduction ratio and crossed angle. However it turns out that the MHI empirical equation provides somehow inaccurate and unsuitable thrust in practical rolling processes. Moreover, we learn that three parameters involved in MHI equation are coupled each other. In this paper, axiomatic design principle is employed to select appropriate parameters involved in approximate equation in order to make parameters uncoupled. A quadratic equation using response surface method with new parameters is suggested. The accuracy of the approximate model is examined by comparing with real experimental data.