We present a straightforward, easy-to-implement, point-based approach for animating elastoplastic materials. The core idea of our approach is the introduction of embedded space —the least-squares best fit of the material's rest state into three dimensions. Nearest-neighbor queries in the embedded space efficiently update particle neighborhoods to account for plastic flow. These queries are simpler and more efficient than remeshing strategies employed in mesh-based finite element methods. We also introduce a new estimate for the volume of a particle, allowing particle masses to vary spatially and temporally with fixed density. Our approach can handle simultaneous extreme elastic and plastic deformations. We demonstrate our approach on a variety of examples that exhibit a wide range of material behaviors.