Currently, the two main approaches to realistic facial animation are 1) blendshape models and 2) physics-based simulation. Blendshapes are fast and directly controllable, but it is not easy to incorporate features such as dynamics, collision resolution, or incompressibility of the flesh. Physics-based methods can deliver these effects automatically, but modeling of muscles, bones, and other anatomical features of the face is difficult, and direct control over the resulting shape is lost. We propose a method that combines the benefits of blendshapes with the advantages of physics-based simulation. We acquire 3D scans of a given actor with various facial expressions and compute a set of volumetric blendshapes that are compatible with physics-based simulation, while accurately matching the input scans. Furthermore, our volumetric blendshapes are driven by the same weights as traditional blendshapes, which many users are familiar with. Our final facial rig is capable of delivering physics-based effects such as dynamics and secondary motion, collision response, and volume preservation without the burden of detailed anatomical modeling.