A new framework for thinking about the deformation behavior of rocks and other heterogeneous polycrystalline materials is proposed, based on understanding the patterns of stress transmission through these materials. Here, using finite element models, I show that stress percolates through polycrystalline materials that have heterogeneous elastic and plastic properties of the same order as those found in rocks. The pattern of stress percolation is related to the degree of heterogeneity in and statistical distribution of the elastic and plastic properties of the constituent grains in the aggregate. The development of these stress patterns leads directly to shear localization, and their existence provides insight into the formation of rhythmic features such as compositional banding and foliation in rocks that are reacting or dissolving while being deformed. In addition, this framework provides a foundation for understanding and predicting the macroscopic rheology of polycrystalline materials based on single-crystal elastic and plastic mechanical properties.