We present a novel technique for generating animation of laughter for a character. Our approach utilizes an anatomically inspired, physics-based model of a human torso that includes a mix of rigid-body and deformable components and is driven by Hill-type muscles. We propose a hierarchical control method which synthesizes laughter from a simple set of input signals. In addition, we present a method for automatically creating an animation from a soundtrack of an individual laughing. We show examples of laugh animations generated by hand-selected input parameters and by our audio-driven optimization approach. We also include results for other behaviors, such as coughing and a sneeze, created using the same model. These animations demonstrate the range of possible motions that can be generated using the proposed system. We compare our technique with both data-driven and procedural animations of laughter.