In the present paper, a new Floating Wave Energy Converter System (FloWECS), consisting of a floating platform and multiple rotating flaps, is proposed and is preliminary investigated. The numerical analysis is implemented in the frequency domain under the action of regular head and oblique incident waves and it is based on a “dry” mode superposition approach. In this approach, the generalized modes concept is utilized for describing the relative to the platform rotation of the flaps, additionally to the six rigid-body modes. The required mode shapes of the generalized modes are determined through appropriate vector shape functions, which are derived in the present paper. The diffraction/radiation problem is solved using a numerical model based on the conventional boundary integral equation method. The proposed numerical formulation is, initially, validated by comparing results with the numerical ones of other investigators for the case of a single, bottom-hinged, rotating plate. Next, the exciting forces and the response of the “isolated” platform are assessed, while, finally, the hydrodynamic behaviour and the energy absorption of the FloWECS are investigated. The results illustrate, that for both examined incident wave directions, the generalized modes’ response and, thus, the system's power absorption is characterized by the existence of distinctive peaks at two different wave frequency ranges, attributed to resonance effects, as well as to the strong interaction effects between the activated flaps.