Abstract: The Hardin-Richart formula used to characterize the very-small-strain stiffness of sands, is mainly based on the experimental data under the isotropic consolidation stress state. The natural soils are anisotropically consolidated. The previous experimental studies have shown that the error of the Hardin-Richart formula will magnify up to 20% as the anisotropic consolidation stress ratio increases. All three different hyperelastic models developed in the soil mechanics literature can reflect the power-law relationship of very-small-strain soil stiffness with respect to the increased mean stress level. But only the HE1 model, accounting for the normal-shear coupling effect including elastic shear dilatation, is capable of modelling the effects of anisotropic consolidation stress ratio on the very-small-strain stiffness. The prediction results of the HE1 model are affected by the values of the model parameters, but generally consistent with the experimental results.