In this article, the hydrodynamics of and nonlinear interaction between the large offshore fish farm “ShenLan 1” and regular waves are investigated using the open-source computational fluid dynamics (CFD) toolbox REEF3D. The framework consists of a rigid body dynamics solver for the frame structure coupled to a fluid solver including the shielding effects of the nets. The solver and grid independence are validated using a 2D numerical wave tank, a free decay test, and a study of the wave loads on a rigid net panel. Then, the effects of regular wave parameters, the thickness of the vertical outer columns of the structure, and the variations of the aspect ratios on the loads, responses, and maximum mooring tension forces are studied. It is concluded that the response motion is sensitive to the wave period rather than the wave height due to the longer duration of unidirectional wave loads acting on the frame. The frequent events of partial submersions and wave overtopping in rather steep waves are confirmed through the capturing of the free surface. The net system accounts for about 30% of the total drag but does not influence the structural response to a larger extend. The effect of the aspect ratio on the hydrodynamics is more distinct than that of the frame thickness. As a result of the study, the first step toward a systemic evaluation of the importance of different structural parts of an offshore fish cage for the expected responses is provided.