A model with deformed atom shells is built to investigate the elastic properties of rare-gas crystals Ne and Kr under high pressure. It is shown that the observed deviation from the Cauchy relation <$Edelta> cannot be adequately reproduced with taking into account of only the many-body interaction. The individual pressure dependence <$Edelta> of is a result of competition of the many-body interaction and the quadrupole interaction associated with the quadrupole-type deformation of electron shells of the atoms during the displacements of the nuclei. Each kind of interaction makes a strongly pressure dependent contribution to <$Edelta>. In the case of Ne and Kr, contributions of these interactions are compensated to the good precision, providing <$Edelta> being almost constant against pressure.

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