Numerical calculations are presented for the contribution of the multipole polarization to the elastic constants in fluorite structure crystals. The multipole polarizability is calculated by the self-consistent field treatment of the local density approximation and the spherical solid model. The elastic constants are significantly affected by the multipole polarization of the ions. The contributions of the multipole polarization of the ions to the elastic constant C-11, C-12, and C-44 are about 25%, 40% and 20% of the experimental values, respectively. The calculated values of the deviation from the Cauchy relation are in good agreement with the experimental values. (C) 2008 Elsevier B.V. All rights reserved.