Recent research work on the slumping-rolling transition of granular solids in rotary kilns is reviewed. A mathematical model is presented for the calculation of critical Froude number. It is supposed that the transition Occurs when the time needed by the propagating avalanche to leave the shear wedge becomes comparable to the time of the shear wedge to be refilled with new particles transported by the rotating wall. It is found that the critical Froude number is proportional to the size ratio d/D (particle to cylinder diameter) and inversely proportional to sin(2) epsilon, where epsilon is the fill angle of the solid bed. Besides the particle diameter, the influence of the bed material needs to be described by only one measurable parameter-the upper angle of repose. To validate the model, the transition behaviour of different bed materials was measured in cylinders of three different sizes. The model is found to predict our measurements as well as those reported in the literature. It is also compared with models from other authors. (c) 2005 Elsevier Ltd. All rights reserved.