We report on a theoretical study of optical extinction in a metal film of 15-230 nm in thickness patterned periodically with sub-wavelength nano-holes of 140 nm in diameter. The gold plate was on a thick SiO2 wafer and the nano-holes as well as the top side of the metal plate were filled with water or solvent. Light was sent in toward the plate from the SiO2 side. The simulations were performed by solving the Maxwell equations using the scattering matrix method. It was seen that the extinction can, depending on the periodicity of the hole array, show one or several peaks in the visible wavelength range. The positions of the peaks were redshifted when the thickness of the gold plate was decreased. It was found that the peak positions for a thick plate can be identified from a simple surface plasmon dispersion relation.