Abstract: This paper presents a method for simulating the two-way interaction between fluids and deformable solids. The fluids are simulated using an incompressible Eulerian formulation where a linear pressure projection on the fluid velocities enforces mass conservation. Similarly, elastic solids are simulated using a semi-implicit integrator implemented as a linear operator applied to the forces acting on the nodes in Lagrangian formulation. The proposed method enforces coupling constraints between the fluid and the elastic systems by combining both the pressure projection and implicit integration steps into one set of simultaneous equations. Because these equations are solved simultaneously the resulting combined system treats closed regions in a physically correct fashion, and has good stability characteristics allowing for relatively large time steps. This general approach is not tied to any particular volume discretization of fluid or solid, and we present results implemented using both regular-grid and tetrahedral simulations.