We propose an effective way to mediate extraordinary optical transmission (EOT) in metallic hole array systems. The EOT phenomena are measured quantitatively by simple calculation which includes the effective values of the optical constants considering finite dimensions of the dielectric layer. The design of dielectric media along the metallic holes plays an important role in tuning the EOT by adjusting the amount of localized charge distribution around the holes. The consistent thickness of the dielectric media surrounding all metal surfaces consequently brings about the surface plasmon resonance at an energy level similar to that in a thin continuous film, and helps to enhance the EOT. The results provide a more plausible explanation to interpret the enhanced EOT mechanism, and will be helpful for designing metallic nano hole structures for use in practical applications with finite dimensions of the systems.