||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. Together with plastic offsets that map embedded space to rest space, the embedded space allows us to robustly estimate the deformation gradient, compute elastic forces, and account for plastic flow. We additionally introduce an estimate for the volume of a particle, opening the door for nonuniform sampling, and describe a technique to increase the robustness of point-based elastic simulation. Our approach can handle arbitrarily large elastic deformations and extreme plastic deformations. Because the approach is point-based, there is no need for complex remeshing-the corresponding operation is a simple neighborhood query in embedded space. We demonstrate our approach on a variety of examples that display a wide range of material behaviors.