The contributions from the multipole polarization of the ions to the elastic constants are calculated for the cesium-chloride structure crystals. The multipole polarizabilities of the ions are calculated by the self-consistent field treatment of the local density approximation and the spherical solid model. The calculated contributions C-M,C-11, C-M,C-12 and C-M,C-44 from the multipole polarization to the elastic constant are about 7, 12 and less than 2% of the experimental values C-E,C-11, C-E,C-12 and C-E,C-44 in the cesium-chloride structure crystals, respectively. The contributions from the multipole polarization to the elastic constants are significant in the silver halide crystals and the fluorite structure crystals which exhibit high ionic conductivity, while they are less significant in the cesium-chloride structure crystals which exhibit low ionic conductivity. It is found that the ionic conductivity correlates with the deviation from the Cauchy relation Delta C-E = C-E,C-12-C-E,C-44, and becomes higher with increasing Delta C-E in the silver halide and alkali halide crystals with positive Delta C-E. The calculated values Delta C-M =C-M,C-12 - C-M,C-44 of the deviation from the Cauchy relation due to the multipole polarization are in reasonable agreement with the experimental values Delta C-E in these crystals. These facts indicate that strong non-central forces due to the induced polarization play an important role in the ionic conductivity. (C) 2010 Elsevier B.V. All rights reserved.