A rigid-plastic rate-independent crystal plasticity model capable of capturing banding in single crystals subjected to homogeneous macroscopic deformation is proposed. This model treats the single crystal as a ‘stack of domains’. Individual domains deform homogeneously while maintaining velocity and traction continuity with their neighbors. All the domains collectively accommodate the imposed deformation. The model predicts lattice orientation evolution, slip distribution, strain localization and band orientation in copper single crystals with imposed plane strain deformation. In quantitative agreement with experimental observations reported in the literature, macroscopic shear banding and regular deformation banding are predicted in initially copper and rotated cube oriented single crystals, respectively, while banding is not predicted in initially Goss oriented single crystals. The model does not, however, predict the experimentally observed orientation of smaller scale dislocation boundaries such as dense dislocation walls.