In this paper, the theoretical justification and the numerical verification of the anomalous scattering from cavities partially filled with metamaterials are presented. A hybrid numerical formulation based on the Finite Element Method (FEM) and on the Boundary Integral (BI) for the analysis of cavity backed structures with complex loading metamaterials is first presented. The proposed approach allows the analysis of cavities filled with materials described by tensorial linear constitutive relations, which may well describe artificial metamaterials synthesized with proper inclusions in a host dielectric. It is found that cavities loaded with pairs of metamaterial layers with "resonant" features possess unusual scattering properties, and with judicious selection of constitutive parameters for these materials the transparency effect or significant enhancement in the backscattering from such cavities are obtained. This may be considered as a first step towards the analysis of the scattering and radiating features of cavity-backed patch antennas and reflect-arrays in presence of multilayered metamaterial loads.