The tumbling mill simulation problem has been intractable due to the multibody collision events involving thousands of balls and rocks. The harsh environment in the mill prevents any intrusion with measuring sensors. Simpler physical models with some empiricism could not describe the charge motion within the mill adequately. The discrete element method (DEM) provides a fitting solution to this problem. In this paper, the formulation of both two- and three-dimensional (2D and 3D, respectively) DEM algorithms for the tumbling mill is presented. Experimental validation of the models is also presented.