[en] The cage compound NdCo₂Zn₂₀ with the antiferromagnetic transition temperature T_N = 0.53 K has the cubic CeCr₂Al₂₀-type structure. The Zn ion at 16c site of this compound is encapsulated in the cage composed of twelve Zn ions at the 96g site and two Nd ions at the 8a site. Since the magnetic susceptibility follows the Curie-Weiss law between 10 and 300 K, the 4f-electrons of Nd³⁺ ions are well localized, and the crystal electric field (CEF) effect may play an important role in the electronic states. To investigate the CEF effect and the rattling motion in NdCo₂Zn₂₀, we measured the transverse elastic modulus C₄₄. The elastic modulus C₄₄ increases monotonically with decreasing temperature down to 40 K, and then it shows an elastic softening below 40 K. The softening does not stop down to 4.2 K. This result can be reproduced by a strain susceptibility above 15 K. The softening of the calculated C₄₄ between 15 and 40 K is due to an indirect quadrupole interaction between the ground doublet and the first excited quartet at 43 K because the ground doublet is the Kramers doublet with no quadrupole degeneracy. No clear elastic anomaly due to the rattling motion expected from the crystal structure was observed in the temperature dependence of C₄₄. (author)