Regarding the storage of nuclear waste within clay rock formations requires fundamental understanding of elastic properties of this rock type with regard to the risk evaluation process. The influence of the pore geometry on elastic properties of Opalinus Clay is studied on the basis of realistic pore microstructure, which is reconstructed from image data acquired by focused ion beam nanotomography. These microstructures are used as input pore geometries for linear elastic finite-element modeling to determine Thomsen’s [Formula: see text], [Formula: see text], and [Formula: see text] anisotropy parameters and the effective elastic moduli related to the porous material. The presence of fully drained intergranular pores substantially increases the values of [Formula: see text] and [Formula: see text]. For the investigated sample with an expected porosity of approximately 10 vol.%, the anisotropic pore space contributes similarly to the anisotropy parameters when compared with the contribution related to the preferred orientation of minerals. On the other hand, if the pore space is undrained, the effect of pores is smaller and the anisotropy is largely controlled by the preferred orientation of minerals. It is revealed that the value of [Formula: see text] is most sensitive to changes in water saturation. In case water is drained from the pores, the vertical Young’s modulus [Formula: see text] reduces significantly more when compared with the horizontal modulus [Formula: see text]. Presuming that the drainable porosity corresponds to a volume fraction of 10 vol.%, [Formula: see text] reduces by approximately 15%–20%. The effect of drainage is even more pronounced for the Poisson’s ratios, whereas the shear moduli are not much affected by drainage.