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This dissertation presents algorithms for the simulation of solids and fluids, and for two-way coupling between the two. Physically-based simulation has a wide range of applications, and the focus in this dissertation is on creating visually plausible animation for computer graphics and visual effects. Novel techniques for rigid body simulation are described first. These include a new approach to time integration, merging it with the collision and contact processing algorithms in a fashion that obviates the need for ad hoc threshold velocities. In addition, a novel shock propagation algorithm allows for efficient use of the propagation (as opposed to the simultaneous) method for treating contact. Examples are given involving many nonconvex rigid bodies undergoing collision, contact, friction, and stacking. A brief overview of existing techniques for simulation of thin deforming shells (such as cloth) is also given. Our fluid simulator is described next. Techniques for both smoke and water simulation are presented, with the latter making use of the particle level set method to represent the water-air interface. A node-based approach is described which allows both uniform and octree grid discretizations to be handled in a consistent and efficient manner. Next, a novel method for coupling infinitesimally thin solids to the fluid is presented. The proposed method works for both rigid and deformable shells. Leaks across the solid are prevented by using robust ray casting and visibility. Incompressibility is properly enforced at the solid-fluid interface so that fluid does not incorrectly compress (and appear to lose mass). Furthermore, computation of a smoother pressure for coupling alleviates some of the stiffness associated with coupling to an incompressible fluid. Finally, coupling to volumetric solids is described. The coupling strategy is similar to that used for thin shells, except ghost values, rather than one-sided stencils, are used to enforce boundary conditions at the solid-fluid interface. In addition, a more accurate approach to computing the coupling pressure is suggested. For both thin shells and volumetric solids, our coupling framework treats the solids simulation as a black box, allowing any alternative simulators to replace the ones used here.