The collision force in a tumbling ball mill was analyzed numemically by discrete element method(DEM). From the frequency distribution of the collision force obtained by the present numerical simulation, the selection and the distribution functions to predict the grinding rate were evaluated. In case of constant rotational speed, the selection functions were almost the same except for the case of the ball filling ratio of 0.1. On the other hand, the selection functions were strongly affected by the rotational speed of the mill vessel in the case of the constant ball filling ratio. The distribution functions showed no significant difference in all conditions. Both functions derived by the present simulation were compared with those obtained from the grinding experiment with measurement of collision energy between the ball and mill wall without powder. The simulated selection and distribution functions were in good agreement with those obtained from the grinding experimental results.