A method that uses both Hartree-Fock and hybrid Hartree-Fock density functional methods at the 6-311 +G(2df,p) basis set level is used to calculate the F-19 NMR chemical shifts for possible Al-F species in sodium aluminosilicate glasses. The accuracy of this method has been carefully checked by calculating F-19 NMR shifts for several well-characterized crystalline materials. Almost all possible Al-F bonding environments in sodium aluminosilicate glasses, including terminal F atoms, corner-shared F species (i.e., both Al-F-Al or Al-F-Si), and edge-shared F species (i.e. Al-(FF)-Al), in 4-, 5-, and 6-coordinated Al species have been investigated. A clear trend is observed between the chemical composition of the environment and the F NMR shift. With more and more bridging 0 atoms in the vicinity, the F atom becomes less shielded, regardless of whether it is terminal or shared. Both Na+-free and Na+-bearing cluster models are used to investigate both this trend and the change in chemical-shift values upon Na+ addition. Terminal F atoms are highly shielded, with chemical shifts from -172 ppm to -216 ppm. Corner-shared F atoms have a broad chemical-shift distribution, from -104 ppm to -197 ppm. Edge-shared F species have chemical shifts from -143 to -172 ppm. Many shared F environments could possibly contribute to the - 147 ppm broad peak that is reported in the F-19 NMR spectra of fluorine-bearing aluminosilicate glasses.