Abstract <p>The results of studying the process of asymmetric rolling using mathematical modeling methods have been presented. Various conditions on the upper and lower surfaces of the rolled product in the deformation zone in the study have been created by lower and upper rolls with barrels of different diameters, which were set to the same angular velocity relative to their rotation axes. An approach that made it possible to establish patterns in the influence of process conditions on the energy-power characteristics of an asymmetric deformation zone has been proposed. As a result, a method for estimating the parameters of the process of asymmetric continuous rolling of a steel strip, which makes it possible to estimate the value of inter-stand tensions with allowance for the circumferential rotation speed of the surface of the barrels of the rolls has been developed. It has been shown that the difference in the diameters of the barrels of the operating rolls has a very small effect on the oscillation of the strip tensions in the inter-stand gaps. A more significant effect on the process parameters is exerted by the average value of the barrel diameters of the upper and lower rolls in the stand.</p>