BeC, a two-dimensional hypercoordinated nanostructure carbon compound, has been the focus of the nanoworld because of its high value of dynamical stability, in-plane stiffness, carriermobility and the existence of band gap. In this work, we have explored the electronic and the optical properties of this material under the influence of static external perpendicular electric field within the framework of density functional theory. Under the influence of a uniformelectric field, the band gap changes within themeV range. The electron energy loss function study reveals that thismaterial has optical band gaps which remain constant irrespective of the applied electric field strength. The optical property also exhibits interesting features when the applied field strength is within 0.4-0.5 V/Å. We have also tried to explain the optical data from the respective band structures and thus paving the way to understand qualitatively the signature of the optical anisotropy from the birefringence study.