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Two-dimensional periodic subwavelength structures have been widely used in various optoelectronic devices. The coupling of electrons and photons is a key factor to be considered and the scattering process of light by the periodic structures has great influence on the optical transmission of these devices. In this work, bilayer metal films patterned with periodic subwavelength holes have been studied using a scattering matrix method [1]. The group theory is also employed in the case when symmetry is present in the systems in order to simplify the calculations. In particular, the optical transmission of bilayer metal films with a periodic array of holes is calculated as a function of the radii of the top and bottom holes, the thicknesses of the two metal layers, and the period of the array. We find that the optical transmission characteristics of the bilayer metal films are closely related to the excitation of surface plasmon polaritons (SPPs) and localized surface plasmons (LSPs).