By means of first-principle FLAPW-GGA calculations, we have investigated the electronic properties of the newly discovered layered quaternary systems SrFeAsF and CaFeAsF as parent phases for a new group of oxygen-free FeAs superconductors. The electronic bands, density of states, Fermi surfaces, atomic charges, together with Sommerfeld coefficients and molar Pauli paramagnetic susceptibility have been evaluated and discussed in comparison with oxyarsenide LaFeAsO - a parent phase for a new class of high-temperature (Tc about 26-56K) oxygen-containing FeAs superconductors. Similarity of our data for SrFeAsF and CaFeAsF with the band structure of oxygen-containing FeAs superconducting materials may be considered as theoretical background specifying the possibility of superconductivity in these oxygen-free systems.