The main causes of seismic anisotropy in sedimentary rocks are the layer-induced anisotropy of finely stratified isotropic rock (fine-layer anisotropy) and the anisotropy due to distributions of stress-aligned fluid-filled micro-cracks (extensive-dilatancy anisotropy). Shear-wave propagation in finely-layered cracked media is characterized by the presence of point singularities, which occur at different directions (incidences and azimuths) of shearwave propagation.