Knowledge of anisotropic elastic properties of shales is important for understanding of shale compaction trends, improved seismic to well tie, nonhyperbolic moveout correction as well as for establishing a baseline for predicting properties of organic-rich shales. So far, however, building a predictive model of elastic properties of shales remains a difficult task. This might be explained by the multiparametric character of such modeling and the fact that the effects of some parameters cannot be measured and are thus poorly understood. The significant number of parameters required for prediction of the elastic properties of shale stems from its multicomponent nature. Shales are nanocomposite materials that comprise phyllosilicate clay particles with a substantial part of their grain size distribution smaller than 2 μm in radius and typically silt particles of quartz and feldspar with grain sizes between 2 and 60 μm (Mitchell & Soga, 2005). The complexity of the system is complemented by pores of micrometer to nanometer scale, whose shape and orientation are seldom characterized (Desbois, 2009). In the smallest of these pores, the filling water contributes to the stiffness and rigidity of the composite via electrostatic and van der Waals interactions (Holt & Kolsto, 2017). Attempts to model elastic properties of shales began with the classic work of Hornby et al. (1994) who modeled shale as a composite material that comprises anisotropic water-saturated clay blocks with a preferred orientation, silt inclusions, and free water. The orientation distribution function (ODF) of the clay crystals was estimated from scanning electron microscopy and the silt fraction from X-ray diffraction analysis or microtomographic images. The other unknown parameters, namely, elastic moduli of the clay blocks, aspect ratio of pores, and the fractions of free water and bound water in the clay blocks became fitting parameters.