Under the harmonic approximation. the contributions from the indirect ionic interactions to the elastic constants are calculated for the alkali halide and silver halide crystals with the rock-salt structure. The coupling constants of the indirect ionic interactions are calculated by the self-consistent field treatment of the local density approximation and the spherical solid model. The calculated values of the coupling constants are large for the silver ion. The indirect ionic interaction significantly affects the elastic constants. It quantitatively explains the deviation from the Cauchy relation in alkali halide crystals. Moreover, it provides a clear account for the large values of the deviation from the Cauchy relation in AgCl and AgBr. (C) 2009 Elsevier B.V. All rights reserved.