Surgical repair of the mitral valve results in better outcomes than valve replacement, yet diseased valves are often replaced due to the technical difficulty of the repair process. A surgical planning system based on patient-specific medical images that allows surgeons to simulate and compare potential repair strategies could greatly improve surgical outcomes. The system must simulate valve closure quickly and handle the complex boundary conditions imposed by the chords that tether the valve leaflets. We have developed a process for generating a triangulated mesh of the valve surface from volumetric image data of the opened valve. The closed position of the mesh is then computed using a mass-spring model of dynamics. In the mass-spring model, triangle sides are treated as linear springs supporting only tension. Chords are also treated as linear springs, and self-collisions are detected and handled inelastically. The equations of motion are solved using implicit numerical integration. The simulated closed state is compared with an image of the same valve taken in the closed state to assess accuracy of the model. The model exhibits rapid valve closure and is able to predict the closed state of the valve with reasonable accuracy.