Two-dimensional structures of 28328 Teflon cylinders with average periodic square and rectangular latticesare prepared. The far-infrared spectra are measured at high-symmetry points of the structures and for s and pwaves, respectively, and the corresponding photonic bands are calculated. In most cases, the agreement between measurements and calculations is good. The influences of disorder upon the transmission spectra are observed. The unexpected transmission dips at the Mpoint of pwave and the very low transmittance in the high-frequency region are discussed.