In this work an emerging hydrokinetic energy technology, Tethered UnderSea Kites (TUSK), is studied. TUSK systems use an axial-flow turbine and generator mounted on a rigid, underwater winged kite that is tethered to a floating surface buoy to extract power from an ocean current. The tethered underwater kite is controlled to travel in cross-current motions at a high velocity which is at least four to five times larger than the ocean current velocity. This higher velocity significantly increases the potential power output compared to conventional fixed marine turbines. Modeling and simulation of the kite-tether dynamics in a TUSK system is studied by developing and solving governing equations of motion derived from Euler-Lagrange equations. Models for physical effects appropriate to TUSK systems are developed, including for turbine power and turbine drag, kite wing hydrodynamic forces, and the effect of turbine blade tip cavitation on turbine power output. A baseline simulation that includes these modeled effects and a simple kite control scheme is studied to estimate cross-current kite trajectories, turbine power output, kite hydrodynamic forces, kite pitch, roll and yaw dynamics, and tether tensions. Once the baseline simulation case has been fully explored, a parametric study is conducted that varies key design and flow parameters including ocean current speed, kite weight and wing area, turbine rotor area, tether length, and kite control system parameters.