This paper describes the development of an underwater cable dynamics model and a realistic control system which allows deployment, regulation, and retrieval of an unmanned underwater vehicle tethered to a ship. An order-n algorithm for a variable mass cable subject to hydrodynamic forces and motion constraints is used to simulate the dynamics of the system. The dynamics of the underwater vehicle is separately given with the cable tension nonlinearly affecting the vehicle speed. This creates a constraint on the cable motion that depends nonlinearly on the constraint force, a problem that is iteratively solved using constraint stabilization. The cable dynamics model and the controller presented in this paper can be used to answer many design questions relating to tethered underwater vehicles.