High speed hammer mills break particles suspended in gas by high velocity impact against a hammer surface. Assuming that the action is comparable to a stream stagnating against a surface, it is shown that the net mill power can be calculated and it is predicted that the power varies approximately proportional to the hammer speed cubed. Literature data on the distribution of particle strength of tested particle sizes were generalized to enable the distribution to be measured for any size. Considering the mill section containing the hammers to be fully mixed, the algorithms are developed to predict the product size distribution under known hammer velocity and exit classification conditions. Particles that are too strong to break under the impact forces, as indexed by specific impact energy, will leave the mill unbroken as "hard" (strong) particles. However, applying the concepts of damage mechanics, the algorithms are modified to allow for weakening of hard material by repeated impacts. Examples show that the predicted change in product size distribution is very significant for a damage accumulation constant appropriate for limestone, and it is concluded that a correct prediction cannot be obtained without allowing for damage. (C) 2004 Elsevier B.V. All rights reserved.