The Micro-Stripes program has been used to calculate resonance wavelengths and the bandwidth of inductive cross-shaped metal meshes in contact with dielectric layers. The shift of the resonance wavelength, depending on the thickness of the dielectric layers, has been studied for two refractive indices. The transmittance of two mesh filters with dielectric spacers or embedded in a dielectric has been calculated for specific alignment of the crosses of one mesh with respect to the other. Transmission line theory has been used to calculate the transmittance of two mesh filters with nonaligned crosses and dielectric layers. A coupled oscillator model has been used for interpretation of the interaction of resonance and Fabry-Perot modes.