Calculation formulas for determining the energy-power parameters of roll mechanisms, such as the forces created by the roll gripping devices, the torque, and the power required to rotate the rolls were derived in the study. It was revealed that the radii of the rolls and the thickness of the processed material have the greatest influence on the energy-power parameters. Reducing the roll radius and material thickness makes it possible to reduce the gripping force related to a decrease in the length of the contact zone. As the radius of the roll decreases, the torque decreases as well due to the decrease in the radius of action of the resulting friction force.