During the last two decades, several studies have shown that organic-rich shales are characterized by strong velocity anisotropy. It is well known that these types of rocks exhibit strong polar anisotropy, also known as vertical transverse isotropy (VTI), with vertical (or bedding-perpendicular) velocities being much slower than horizontal (or bedding-parallel) velocities. However, the amount of elastic anisotropy can vary significantly from one formation to another because the individual clay minerals, the volume concentration and geometric distribution of organic matter, and other geologic characteristics (such as texture and nonclay mineralogy) vary by geologic formation. It is therefore important to quantify the amount of elastic anisotropy in our formations of interest, for various geophysical and geomechanical applications related to reservoir characterization. Strongly anisotropic compressional and shear velocities in two formations of interest in an unconventional reservoir are analyzed. Appropriate rock-physics models explain the anisotropic elastic response of these rocks. Recognizing that there might be several possible sources of anisotropy, three sources are focused on: mineral orientation, layering, and microcracks. Preferred orientation of clay minerals is the largest and most significant source of elastic anisotropy in the samples.