The purpose of this work is to develop advanced numerical tools for modeling two-way fully nonlinear interactions of ocean surface waves (irregular waves in the general situation) with submerged structures undergoing large amplitude motion, that could represent Wave Energy Converters (WECs). In our modeling approach, an existing two-dimensional Numerical Wave Tank (NWT), based on potential flow theory, is extended to include a submerged horizontal cylinder of arbitrary cross-section. The mathematical problem and related numerical solution are first introduced. Then, conservation of volume and conservation of energy are checked, respectively, in the case of a circular cylinder in a prescribed large amplitude motion and in the case of a circular cylinder in a free motion. Interactions between waves and a submerged circular cylinder computed by the model are then compared to mathematical solutions for two situations: a cylinder in prescribed motion and a freely moving cylinder.