Structural properties of the (NaCl-type) and (CsCl-type) phases of alkaline-earth oxides and their phase transition have been investigated with the periodic ab initio linear combination of atomic orbitals method implemented in the CRYSTAL program. The geometries have been optimized and the bulk modulus evaluated. The calculations have been done at the Hartree-Fock (HF) and density functional theory (DFT) levels. In this last case, the exchange-correlation potential correcting the electronic density uses either one local or three non-local models. The comparison of the different approaches allows us to identify a trend, in order to obtain results in better agreement with experiment.