Mathematical models of grinding mills and crushers are undergoing significant advances in recent years, demanding ever more detailed information characterizing ore response to the mechanical environment. In a mechanistic model of a comminution machine, the type of characterization data used should cover, as much as possible, the conditions found inside the size reduction machines. This applies to the particle size, the stressing energy and rates that particles are subject to, the breakage mechanism and the level of interaction of the particles during stressing, which all must be described appropriately. Whereas, a very large number of experimental techniques and published data exist that allows understanding and quantitatively describing the response of single particles to stressing, comparatively little information exists on the breakage of particles contained in beds. The present work investigates breakage of particle beds impacted by a falling steel ball in unconstrained conditions, such as those that are likely to be found in tumbling mills. The influences of particle size, impact energy, ball size and bed configuration are investigated for selected materials and a mathematical model is proposed that describes the influence of all these variables. The key element of this model is that it allows predicting breakage in monolayer unconfined particle beds with a combination of single-particle breakage data and functions that describe energy partition and volume of material captured in the bed. This model has been calibrated and validated using data from quartz, granulite, limestone and a copper ore, with good agreement. (C) 2010 Elsevier Ltd. All rights reserved.