Abstract: A friction element with a rigid scrface is constricted, and a finite element model of a friction-drive vertical roll in universal roiling is established. In the model, a layer of friction elements is placed between the flange of the stock and the vertical roll. By rigidizing the friction element surface that adheres to the vertical roll, a rigid vertical roll is virtually simulated, so that the vertical roll velocity is incorporated into the variables to be solved by finite element equations. It overcomes the solution difficulties brought about by the unknown vertical roll velocity. The model is able to directly obtain the velocity of the vertical roll, instead of assuming it a priori and calculating it iteratively. Numerical examples show that the model meets the requirement of zero torque and rigidity for vertical roll.