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Photonic Band Gap (PBG) structures are periodic lattices of dielectric or metallic inclusions which provide an effective way to control and manipulate electromagnetic radiation. These periodic structures have some allowed and forbidden frequency bands and this forbidden region known as ??Photonic or Electromagnetic Band Gap??. In this paper, the dispersion relation of the two dimensional metallic photonic band gap structure is analyzed using the plane wave expansion (PWE) method for both TE and TM modes of propagation. The dielectric function of the metal from which cylinders are formed, has free electron model ??(??) = 1-(??2 p/??2) where ??p in the plasma frequency of conduction electron. Dispersion relation for square lattice as well as triangular lattice were derived and plotted. This clearly exhibits the pass band and stop band of the PBG structure. We analyzed the filling factor on band structure for both polarizations.