We formulated a novel method to calculate the dispersion relations of arbitrary photonic crystals with frequency-dependent dielectric constants based on the numerical simulation of dipole radiation. As an example, we applied this method to a two-dimensional square lattice of metallic cylinders and obtained a good agreement with the previous result by means of the plane-wave expansion method by Kuzmiak et al. [Phys. Rev. B 50, 16 835 (1994)]. In addition to the dispersion relations, we could obtain the symmetries and the wave functions of the eigenmodes.