We study the problem of scattering by a thin and conducting screen perforated periodically with square apertures, when the screen is illuminated by an electromagnetic wave in subwavelength regime. Our formulation extends the monomodal approximation technique up to the second-order Floquet modes, which enable us to investigate not only propagation mode, but also nonpropagation mode in the low-frequency regime. We also study dispersion relation of the principal Floquet modes and show the behavior of electromagnetic fields in the periodic system at the extremely low frequency, the resonance frequency and Wood’s anomaly frequency. The interesting characteristics of the fields can be found in these specific frequencies.