NMR signals of 7Li, 23Na, 35Cl, 39K, 79Br, 87Rb and 127I have been measured in various alkali and halogen salt powders relative to well defined aqueous solutions. With the known shielding constants of some of these solutions the nuclear magnetic shielding constants of the alkali and chlorine nuclei in crystalline powders were evaluated in the atomic reference scale. The theoretical values of the shielding constants in alkali halides do not agree even in the order of magnitude with the experimental ones in some cases.For 23Na first-order and second-order quadrupole patterns have been observed and the quadrupole coupling constants are given.