A model of grinding with particle interaction taken into account has been constructed. A variant of the interaction has been analyzed which is due to the falling of small particles into the vacancies between the large ones. The particle interaction has been used to explain the formation of a size distribution that has few maxima. Within the scope of the model both the share of the small particles and the ratio of the size corresponding to the maxima are deduced, which both proved to be close to the values observed experimentally. Grinding kinetics have been described by the batch grinding equation with the selection function dependent on the current distribution. Methods of modifying the selection function have been discussed and, for some of them, numerical simulations have been performed.