The structural, electronic and elastic properties, as well as the IR and Raman central zone phonon frequencies of CaF2, SrF2 and BaF2, have been evaluated by using the periodic ab initio linear combination of atomic orbitals method implemented in the CRYSTAL package. The Hartree-Fock and different density functionals, namely the local density (LDA) and the generalized gradient (GGA), as well as the hybrid B3LYP, Hamiltonians, have been used. The binding energy, equilibrium lattice parameter, elastic constants (C-ij) and central zone phonon frequencies exhibit a regular and consistent trend in the series, in good agreement with experimental data. (C) 2002 Elsevier Science B.V. All rights reserved.