A model different from the traditional WEC, known as the flexible wave energy converter (fWEC), is numerically modeled in this paper. The fWEC is believed to be more efficient and has a greater range of operation when compared with the conventionally rigid WEC. A fully coupled fluid–structure interaction (FSI) tool is developed for the research performed in this paper. This tool is able to accommodate the dynamic interaction between the flexible membrane structure of the fWEC and the surrounding fluid. In this research, both linear-elastic and hyper-elastic materials are examined for their use in the fWEC. The fluid flow surrounding the fWEC is solved by a computational fluid dynamics (CFD) method. The deformation of the hyper-elastic structure within the fWEC is modeled using a finite element analysis method (FEA). Both the hyper-elastic material of the fWEC and the free surface wave contribute to the overall nonlinearity of the numerical simulation. To tackle this problem, a robust coupling scheme is implemented by an advanced coupling library. With this tool, the flexible deformations within the fWEC structure can be accurately captured. The degree of these deformations can then further be examined, allowing the overall effects on the fWEC energy output to be determined. The simulation results show that the peak deformation of the hyper-elastic material is four times that of the linear-elastic material. This suggests that the fWEC would perform better and generate greater power using the hyper-elastic material compared with the linear-elastic material. Additionally, because a wide range of wave conditions are studied, it can be concluded that unlike conventional WECs, the efficiency of energy harvesting of such an fWEC is not sensitive to certain wave periods. Such findings are supported by both the detailed flow fields captured and the structural stress–strain analysis results from this simulation.