The full set of transversely isotropic elastic stiffness constants of inorganic shale (mudrock with total organic carbon less than 1.5%) can be successfully modeled and, therefore, predicted based on the mineral composition, mineral stiffnesses, clay platelet orientation distribution function, and microgeometry of the pore space. A fundamentally novel concept drawing from the Maxwell homogenization scheme allows a zero-porosity mineral matrix of the mudrock to be expressed as a polycrystal of variable composition and clay mineral alignment. Introduction of the brine-saturated pore space allows us to account for realistic 3D pore types and their combinations as well as elastic interactions, opening the way for better integration of rock physics and geomechanics with modern petrographic investigations and better shale velocity/anisotropy prediction as a function of diagenetic porosity reduction. We were able to calibrate the model using a limited subset of high-quality ultrasonic measurements on shale and constrain main pore geometries such as tetrahedra and irregular spheroids, often reported in modern scanning electron microscopy images. The model is then used to constrain the anisotropy tensor elements of illite-dominated clay, impossible to measure directly, and explore the main compositional and microstructural controls on the anisotropic elasticity of inorganic shale, including the most troublesome stiffness and its derivative — the anisotropy parameter , which is of paramount importance in quantitative seismic interpretation.