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Sensing with sub-wavelength hole arrays is being actively researched as a means to improve detection sensitivity and reduce the size of the developed sensor. One of the approaches to sensing with hole arrays is to use a shift of the main transmittance peak generated by analyte exposure. In this report, the effect of the shape of the holes on the peak shift is investigated with a view to improve further the main transmittance peak shift. Rectangular holes are studied by simulation and experiments with a palladium metallic matrix. Palladium permittivity is varied by exposure to hydrogen and generates main transmittance peak shifts toward longer wavelengths. The simulation results of the propagation constant and electric field distribution revealed that the peak shift is controlled by the short side length of the rectangular holes. The short side of the rectangular holes normalized by the peak wavelength should be below 1/10 for the rectangular holes to achieve their maximum effect.