We present a study of the structural, electronic, elastic and vibrational properties of the rhombohedral BiAlO3 structure within the local density approximation of density functional theory using norm-conserving pseudopotentials. The calculated equilibrium lattice constant, angle and atomic position are in reasonable agreement with the available experimental and theoretical dates. Based on the elastic constants and their related parameters, the crystal mechanical stability have been discussed. The elastic constants for BiAlO3 are also needed to completely determine its elastic properties including polycrystalline bulk, shear and Young's moduli, Poisson's ratio and the elastic anisotropy. Energy band structure shows that the rhombohedral BiAlO3 has an indirect band gap between D and U-D symmetry points. We compute Born effective charge tensor, which is found to be quite anisotropic of Bi and O atoms. BiAlO3 have been studied by applying the direct method and deriving the phonon dispersion relations which include the longitudinal/transverse optical phonon mode splitting. In the rhombohedral phase the phonon dispersion curves show a soft mode between X and U-point. This soft mode leads to the observed rhombo-hedral-cubic phase transition. The results are compared with the previous calculations and available experimental data. Crown Copyright (C) 2013 Published by Elsevier B.V. All rights reserved.