In this paper, asymmetric cold rolling is simulated using an explicit analysis procedure. A two-dimensional finite element model with an adaptive meshing technique has been employed to simulate asymmetrical condition due to the difference of the roll radius and velocity. Some conditions have been found to make sheet without curvature; in order to achieve this goal, different velocities have been considered in rolls in each radius ratio. To validate the simulation, the results of the simulation have been compared with experimental papers, as done in the past. The effects of asymmetric process, caused by radius ratio and velocity ratio, on the rolling force, rolling torque, and the sheet curvature have been analyzed and discussed. In addition, the optimum velocity ratio in each radius ratio that causes the sheet without curvature has been obtained. It has been found that an appropriate speed ratio to produce flat sheets (i.e., sheets without curvature) is almost 1.067, independent of the radius ratios between 1 and 1.05. (C) 2018 Sharif University of Technology. All rights reserved.