GaN and AlN have attracted a great attention in the photonics researches. The large band gaps of these materials turn them suitable for nanophotonic devices that operate in light ranges from visible to deep ultraviolet. The photonic band gap maps obtained from plane wave calculations of common structures in wurtzite GaN and also in AlN were presented and analyzed. A complete photonic band gap with flat bands in the M - K direction was observed in the triangular lattice of air holes in dielectric medium.