In this study, a semi-analytical solution is developed to investigate the wave interference and corresponding dynamic responses of an array of submersible flexible fish cages. The net chamber is modelled as a perforated cylindrical shell, and the penetration flow through the cage interface is described by a porous medium model. Based on the potential flow theory, the solution to this physical problem is expanded as a series of eigenfunctions in the local coordinate system of each cage, and the scattered wave potentials generated by all cages are superimposed wherein Graf's addition theorem is employed for the coordinate transformation. The mean wave drift effect is also explored, which is a nonlinear phenomenon derivable from the first-order solution. The results indicate that the interference of waves is determined by wavenumbers, cage spacings or net porosities, and significant wave responses are manifested near the top part of the cage. Additionally, the first-order wave force vanishes at a ratio of cage diameter to wavelength = 0.59, and, along the direction of wave incidence, the rear cages experience opposite mean wave drift loads relative to those on the front cages. These studies provide benchmark results for understanding the hydroelastic characteristics of multi-cage systems.