The estimation of illite-rich shale anisotropy to account for the alignment of clays and gas- or brine-filled cracks is presented via mathematical modelling. Such estimation requires analysis to interpret the dominance of one effect over another. This knowledge can help to evaluate the permeability in the unconventional reservoir, stress orientation, and the seal capacity for the conventional reservoir. Effective media modelling is used to predict the elastic properties of the illite-rich shale and to identify the dominant contributions to the shale anisotropy. We consider two principal reasons of the shale anisotropy: orientation of clay platelets and orientation of fluid-filled cracks. In reality, both of these two factors affect the shale anisotropy. The goal of this study is, first, to separately analyse the effect of these two factors to reveal the specific features in P- and S-wave velocity behaviour typical of each of the factors, and, then, consider a combined effect of the factors when the cracks are horizontally or vertically aligned. To do this, we construct four models of shale. The behaviour of P- and S-wave velocities is analysed when gas- and water-filled cracks embedded in a host matrix are randomly oriented, or horizontally or vertically aligned. The host matrix can be either isotropic or anisotropic (of VTI symmetry). In such a modelling, we use published data on mineralogy and clay platelet alignment along with other micromechanical measurements. In the model, where the host matrix is isotropic, the presence of a singularity point (when the difference VS1 - VS2 changes its sign) in shear wave velocities is an indicator of brine-filled aligned cracks. In the model with the VTI host matrix and horizontally aligned cracks filled with gas, an increase in their volume concentration leads to that the azimuth at which the singularity is observed moves toward the symmetry axis. In this case, if the clay content is small (around 20 per cent), the singularity point may even vanish. The Thomsen parameters are helpful in fluid type indication in shale. An indicator of gas-filled aligned cracks is ?? > ??. If aligned cracks in illite-rich shale are brine-filled, ?? < ??. Negative value of ?? indicates brine-filled cracks in illite-rich shale. A shale with brine-filled cracks exhibits higher Vp/Vs ratio in the vertical direction as compared to the gas-filled shale. A disorientation of clay platelets and brine-filled cracks may lead to that the singularity point is absent for brine-saturated shale as well. In this case one can also observe ?? > ?? and decreased values of Vp/Vs in the vertical direction as in the case of gas-filled cracks. In the presence of vertically aligned cracks, shales exhibit distinctly revealed features of orthorhombic symmetry. The results have important applications where seismic measurements are applied to predict the maturity state of the shale. ?? 2009 The Authors Journal compilation ?? 2009 RAS.