We have performed ab initio molecular orbital calculations on a cluster of atoms modelling the medium-range structure in Na2O . 3B(2)O(3) glass at the Hartree-Fock/3-21G(*) level. It is shown that the optimized structural parameters are in good agreement with the observed ones. Using the optimized cluster, we have further carried out a vibrational analysis to interpret the far infrared vibrational spectra observed for sodium berate glasses. The frequency calculations of the cluster successfully reproduce the observed far infrared asymmetric absorption profiles which can be deconvoluted into two broad bands. According to the normal coordinates calculated, the two absorption bands are attributed to two different types of vibrations of alkali cations in their anionic sites whose vector displacements are almost perpendicular to each other.