Abstract：The eigenmatrix for the propagation of light in a photonic crystal is obtained by the plane-wave expansion method. Dispersion curves of photonic crystals of two dimensional square and triangular lattices composed of circular air cylinders are calculated numerically under vertical incidence, together with the dispersion curves of two dimensional photonic crystals with different radii of holes. It is shown that the first band gap of E wave of the two dimensional square lattice divides in direction <11>, and so does that of H wave; in direction <10>, the first band gap of E wave is a little smaller than that of H wave and becomes wider with the increase of the radius of the hole; on the other hand, that of H wave becomes wider first then decreases. The edge of the first band gap in direction <11> of two dimensional triangular lattice, different from that of the square lattice, is at point (0.5, 0.5) instead of at point (1, 1); the center frequency is smaller than that in direction <10> and the band gap is larger than that of the square lattice. In direction <10>, the first band gap of E wave is a little wider than that of H wave, and their variation trends are completely different: the first band gap of E wave becomes wider with the increase of the radius of the hole at the first and then decreases, but that of H wave is getting wider all the time.