Discrete models are an effective method to study mixing of granular materials in a variety of cases. We study the mixing of monodisperse granular materials in 2D tumblers rotating in the avalanching regime using two different discrete models. First, we develop a cellular automata (CA) model based on comparing the heights of columns of particles in the CA grid that results in irregular avalanching and mixing of particles. Second, we use a model based on mapping of wedge regions that has been shown to reproduce experimental results. We compare mixing of like particles in tumblers of various shapes and fill fractions using both models. Mixing rates for half-full tumblers demonstrate a strong dependence on the symmetries of the tumbler shape. More than half-full tumblers give rise to a core of unmixed particles with a shape that changes with fill fraction. This results in multiple extrema in the mixing rate depending on the fill fraction. Mixing is fastest for low fill fractions, and triangular tumblers provide the quickest mixing. While the wedge and CA models produce quantitatively similar results, the cellular automata model is substantially more flexible and typically runs in an order of magnitude less time. (c) 2007 American Institute of Chemical Engineers.