The interaction of an incident plane wave with a metamaterial periodic structure consisting of alternating layers of positive and negative refractive index with average zero refractive index is studied. We show that the existence of very narrow resonance peaks for which giant absorption - 50% at layer thickness of 1% of the incident wavelength - is exhibited. Maximum absorption is obtained at a specific layer thickness satisfying the critical coupling condition. This phenomenon is explained by the Rayleigh anomaly and excitation of Fabry Perot modes. (read more)