The two methods of artificial damping and artificial stiffness are developed in dynamic explicit FEA code for ring rolling. Advantages and disadvantages of artificial damping method and artificial stiffness method are analyzed. A rectangular section cold ring rolling is simulated. The hourglass energy and the ratio of the hourglass energy to the internal energy are compared between the two hourglass control methods. The hourglass control coefficient criterion of the two methods in the cold ring rolling simulation is proposed.