The gravity wave interaction with a flexible membrane placed at a finite distance from the partially reflecting seawall is analyzed under the framework of linear water wave theory using the multi-domain boundary element method (BEM). The flow through a flexible membrane is assumed to follow Darcy’s law in addition to membrane displacements. As a viable alternative to the existing wave dampers, the flexible membrane is examined for the effective dampening of incident waves. The correctness of the numerical results is affirmed with the known results available in the literature. The effect of membrane tension, submergence depth, membrane width, porosity, angle of inclination, and confined chamber spacing on hydrodynamic coefficients is discussed as a function of dimensionless wavenumber. The partially reflecting harbor wall diminishes the wave reflection coefficient in the long-wave regime. The increase in the flexible membrane width does not necessarily ensure the ideal wave capturing performance. A shift in the peak of the maximum deflection is observed with the increase of membrane width while there is a shift in peak outward for the increase in the submergence depth. Moreover, the maximum deflection is found to decrease with the increase in porosity, and it is 62% reduction for membrane porosity b = 1 due to the significant wave damping. The wave run-up and the wall force coefficients are found to be minimum when the relative plate width is B/h = 1. The present study is expected to be useful for the design of cost-effective wave attenuating systems.