The dynamic motion of tethered undersea kites (TUSK) is studied using numerical simulations. TUSK systems consist of a rigid-winged kite moving in an ocean current. The kite is connected by tethers to a platform on the ocean surface or anchored to the seabed. Hydrodynamic forces generated by the kite are transmitted through the tethers to a generator on the platform to produce electricity. TUSK systems are being considered as an alternative to marine turbines since the kite can move in high speed motions to increase power production compared to conventional marine turbines. The two-dimensional Navier-Stokes equations are solved on a regular structured grid that comprises the ocean current flow, and an immersed boundary method is used for the rigid kite. A two-step projection method along with Open Multi-Processing (OpenMP) is employed to solve the flow equations. The reel-out and reel-in velocities of the two tethers are adjusted to control the kite angle of attack and the resultant hydrodynamic forces. A baseline simulation was studied where a high net power output was achieved during successive kite power and retraction phases. System power output, vorticity flow fields, tether tensions, and hydrodynamic coefficients for the kite are determined. The power output results are in good agreement with established theoretical results for a kite moving in two dimensions.