The B36N36 fullerene-like cage structure was proposed as candidate structure for the single-shell boron-nitride cages observed in electron-beam irradiation experiment. We have performed all electron density functional calculations, with large polarized Gaussian basis sets, on the B36N36 cage.We show that the cage is energetically and vibrationally stable. The infra-red, Raman and optical spectra are calculated. The predicted spectra, in combination with experimentally measured spectra, will be useful in conclusive assignment of the proposed B36N36 cage. The vertical and adiabatic ionization potentials as well as static dipole polarizability are also reported. [3,4,5,6,7,8,9,10].On the experimental side, there are also a few reports of synthesis of hollow BN structures [10,11,12,13,14].In a series of experiments by Oku and coorkwers, boron nitride clusters of different sizes were reported [10,11,12].Perhaps the most interesting result of these works was the production of B 24 N 24 in abundance. We performed theoretical calculations [8,9]