Offshore wind is a valuable source of renewable energy, as it is typically strong and steady. Turbines have been utilized offshore in parts of Europe and Asia, however only at shallow depths. Floating wind turbines must be implemented in deeper areas to be economical, but this technology is relatively new and untested. This paper describes a numerical analysis model that can be used to investigate the motion of a 5 MW floating turbine subjected to ocean conditions. Prototype designs for a spar buoy and barge platform are studied. The stiffness and damping effects brought about by the mooring lines are evaluated using a dynamic cable model. A boundary element model is used to calculate added mass and damping effects, as well as the forces on the structure caused by the wave-body interaction. The governing equations of motion include all the added mass, damping and stiffness components in the frequency domain. Response of the structure is found by solving the governing equation combined with a wave spectrum to represent actual ocean wave fields. Approximate bending moments at the base of each design are found by inputting the predicted base motion into a linear modal analysis model created in SAP2000. Based on the results found in this paper, incoming waves cause much greater motion of the barge design, especially in the pitching direction.