Transfer matrix method (TMM) is used to study the transmission properties of photonic crystals. The Mur absorbing boundary and periodic boundary are used respectively to truncate the computational region in photonic crystals. For two dimensional square lattice photonic crystals, the transmission coefficient versus the frequency of E-polarized incident electromagnetic waves propagating in photonic-band-gap structures is calculated in perfect periodic structures. A model of 2-D square lattice photonic crystals is designed and fabricated in microwave wavelength regions. The results of numerical simulation are in good agreement with experimental results. And also the properties of transmission are studied in 2-D loss, dispersive and absorbing materials of photonic crystals. And how the photonic band gaps are affected by loss and the dispersive absorbing materials of photonic crystals is investigated.