In this text book, mathematical formulations for the dynamics of raising sunken vessels using buoyant systems are developed in a form which is suitable for integrating control techniques to ensure both hydrodynamic and structural stability for a safe and stable salvaging operation based on both rigid body modeling and flexible body modeling concepts. Due to the coupled nature of salvage dynamics and for integrating controller techniques, the mathematical modeling is carried out as two subsystems. In the primary model, the salvage dynamics is formulated in such a way that the variation in additional buoyancy due to flow rate of filling gas inside the lift bags is the controlling force with respect to hydrostatic force due to weight, buoyancy and suction break out, hydrodynamic forces and uncertainty arises due to any external disturbances. In the secondary model, the purging of gas through the valves is taken as the control parameter by accounting the excess buoyancy available after suction break out and to the variation in pressure difference between gas inside lift bag and surrounding sea water pressure for a stable ascent.