We consider the long-wavelength limit for two-dimensional photonic crystals - periodic arrangement of magneto-dielectric rods with dielectric and magnetic constant ε
embedded in a magneto-dielectric background (ε
). Using the Fourier expansion method in the low-frequency limit (ω → 0 ) we develop an effective medium theory and give a rigorous proof that, in this limit, a periodic medium behaves like a homogeneous one. We derive compact analytical formulas for the effective index of refraction of a 2D photonic crystal. These formulas are very general, namely the Bravais lattice, the cross-sectional form of cylinders, their filling fractions and the dielectric and magnetic constants are all arbitrary. For non-magnetic materials, μa
= 1, we show how to introduce index ellipsoid and demonstrate that the E-mode is an ordinary wave and the H -mode is an extraordinary wave. For magnetic materials the both modes turn out to be extraordinary. This unusual property is unknown for natural crystals.