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In this paper, based on the slab method and focusing on the rate-dependent flow condition, asymmetrical thermomechanical rolling (ATMR) is investigated to establish a new model for calculation of the rolling force. Unlike the former models where the rate-dependent condition of the yield shear stress has not been considered, in this study, a visco-plastic flow stress formulation of material is used for applying the rate and temperature sensitivity parameters and kinetic of work hardening and softening of the material. Comparison of the present analytical model with experimental data and other models reveals the precision of calculation. An asymmetrical rolling index (ARI) is introduced to evaluate the effects of rolling parameters on asymmetrical conditions of the rolling process. Using the response surface methodology (RSM), the interaction effects and contribution of rolling parameters are studied. Investigations indicate that the speed rate plays a role as an intensifier of the parameters' effect on the ARI. Furthermore, the occurrence of high value of speed rate with a low percent of thickness reduction leads to the restricted rise of the ARI levels. The verification of the statistical models indicates an acceptable competency of results. [ABSTRACT FROM AUTHOR]