We investigate the effectiveness of a porous box in attenuating the structural response of a very large floating structure (VLFS). Assuming the water depth to be finite and small amplitude water wave theory, the physical problem is formulated by employing Darcy’s law for flow past a porous structure. The boundary value problem is reduced to a system of linear algebraic equations with the aid of matched eigenfunction expansion method. Further, these simultaneous equations are solved numerically to compute physical quantities. The mathematical model is validated through a comparison with the theoretical results available in the literature. The reflection, transmission, and dissipation coefficients, elastic plate deflection, forces acting on the box, and free-surface elevation are computed. The reflection, transmission, and dissipation coefficients exhibit an oscillatory pattern for large values of wavenumber irrespective of the structural parameters of the box. It is highlighted that a porous box with moderate values of the porous-effect parameter is effective in reducing strain and shear force on the VLFS. Further, the results on elevation and VLFS deflection depict that the suitable porous-effect parameter values for the box reduce the resultant wave amplitude of the elastic plate deflection as well as the amplitude in the lee side of the VLFS. The study reveals that the width and height of the porous box are critical toward the trapping of incident waves inside the box and dissipating the maximum amount of incident wave energy in reduction of wave transmission in the lee side of the structure and thereby attenuating the structural response of the VLFS.