Surface shape control techniques are applied to many diverse disciplines, such as adaptive optics, noise control, aircraft flutter control and satellites, with an objective to achieve a desirable shape for an elastic body by the application of distributed control forces. Achieving the desirable shape is influenced by many factors, such as, actuator locations, sensor locations, surface precision and controller performance. Building prototypes to complete design optimizations or controller development can be costly or impractical. This shortfall, puts significant value in developing accurate modeling and control simulation approaches. This thesis focuses on the field of adaptive optics, although these developments have the potential for application in many other fields. A static finite element model is developed and validated using a large aperture interferometer system. This model is then integrated into a control model using a linear least squares algorithm and Shack-Hartmann sensor. The model is successfully exercised showing functionality for various wavefront aberrations. Utilizing a verified model shows significant value in simulating static surface shape control problems with quantifiable uncertainties. A new dynamic model for a seven actuator deformable mirror is presented and its accuracy is proven through experiment. Bond graph techniques are used to generate the state space model of …