The discrete element method (DEM) has emerged as a powerful tool for simulating discrete particle systems. It has wide application in the field of mining and mineral processing where it can be used as a design and diagnostic tool for industrial size tumbling mills. The simulation of tumbling mills involves the calculation of contact forces between the colliding balls in order to predict the enmasse charge motion, ball wear, power draw, collision spectra, etc. These calculations are made by modeling the contact by a set of spring, dashpot and slider elements. The manner of implementation of these contact elements within the DEM framework and the associated contact parameters determine the accuracy of the simulation. A physically more realistic contact model based on theoretical contact mechanics is described. The model is not implementation specific and requires only material parameters that may be obtained from standard tests. In addition, the model allows for a variation in the coefficient of restitution as a function of impact velocity. The implementation of this contact model is illustrated by simulating a 0.545 m diameter ball mill.