In contrast to dielectric photonic crystals, the propagation characteristics of metallic photonic crystals are of great importance in millimeter wave and submillimeter wave applications. It is convenient and reliable to get the band diagrams and field distributions of photonic crystals after solutions of the eigenmode equations, which is derived from the Yee-mesh-based finite-difference frequency-domain method. However, this method cannot be used for the analysis of metallic photonic crystals because of the essential distinctions between metal and dielectric. Based on this method, we derive eigenmode equations for two-dimensional metallic photonic crystals by introducing the metal surface boundary conditions. And then, after some numerical calculations, the transverse electric mode and the transverse magnetic mode global band gaps of different lattice structures are obtained, including both square lattice and triangular lattice. Finally, we discuss the advantages of metallic periodic structures in mode selection and device integration by the comparison between metallic photonic band gap and dielectric photonic band gap.