The “C-Plane” is a submerged variable depth ocean current turbine that is tethered to the sea floor and uses sustained ocean currents to produce electricity. As part of the development of a 1/30th scale physical model of the C-Plane, a mathematical model and dynamics simulation of the prototype was developed and is presented in this paper. This three-dimensional mathematical model represents the C-Plane as a rigid body with moveable control surfaces that is moored with three linear elastic cable elements. Gravitational, buoyancy, hydrodynamic, cable, gyroscopic, and inertial forces are included and a PC-based dynamics simulation is created. The simulation demonstrates that the C-Plane is stable and capable of changing depth in all expected operating conditions. The C-Plane prototype can fly level from a height of 3 to 6 m using the configuration suggested in this paper. The maximum ascent rates of the C-Plane with a water speed of 0.3 m/s are 0.015 m/s when the pitch is fixed at 0° and 0.030 m/s when the pitch is fixed at 4°. The maximum descent rates of the C-Plane are 0.018 m/s when the pitch is held at 0° and 0.031 m/s if the pitch is held at −4°.