Relating subsurface stress to velocity anisotropy can provide quantitative insight into the effects of reservoir production. Rock-physics models using effective medium theory for unconsolidated sands can be built to establish this link, although empirical corrections are often required. In pursuit of this goal, fractional changes in elastic moduli have been related to fractional changes in stress through a perturbation analysis of the extended Walton model. The stress path considered was composed of isotropic loading followed by an arbitrary stress perturbation. The coefficients derived are dependent on granular elastic moduli and the proportion of grains with no-slip contacts but are conveniently independent of strain and porosity. A modification of these relationships has been introduced using an anisotropic stress-dependent coordination number, whose parameters can be derived from isotropic moduli-stress experiments. The inclusion of an anisotropic coordination number improved the model’s fit to experimental results of unconsolidated sands subject to anisotropic loading.