Many asteroids are thought to be particle aggregates held together principally by self-gravity. Here we study-for static and dynamical situations-the equilibrium shapes of spinning asteroids that are permitted for rubble piles. As in the case of spinning fluid masses, not all shapes are compatible with a granular rheology. We take the asteroid to always be an ellipsoid with an interior modeled as a rigid-plastic, cohesion-less material with a Drucker-Prager yield criterion. Using an approximate volume-averaged procedure, based on the classical method of moments, we investigate the dynamical process by which such objects may achieve equilibrium. We first collapse our dynamical approach to its statical limit to derive regions in spinshape parameter space that allow equilibrium solutions to exist. At present, only a graphical illustration of these solutions for a prolate ellipsoid following the DruckerPrager failure law is available (Sharma et al. BAAS 37 [2005a]