A new approach is proposed to model the bulk movement of solids in rotary drums operating at low rotation speeds, in slumping and rolling regimes. The model yields an equation similar to Saeman's equation, but which is valid also for the slumping regime and active area in the rolling regime. The model was developed for constant depth using a control surface containing the steepest descent direction, so that any contribution from sliding particles to flow rate can be neglected. By considering an appropriate virtual kiln, the model is extended to the more general, variable depth situation.