Natural rocks usually contain discontinuities of various forms, which control fluid moment in the subsurface. Discontinuities have a wide range of scales and are a direct consequence of Earth's stress over geological history, such as faults, fractures, joints or cracks, or are due to sedimentary deposition processes, such as contact regions in pore spaces (examples include clay platelet alignment in shales and grain particle alignment in sandstones). In this study, we show that seismic waves are sensitive to fluids contained in rock discontinuities based on P and converted PS AVO analysis. We restrict ourselves to two types of rock discontinuities: shales where clay particle alignment will result in transverse isotropy with a vertical symmetry axis (TIV) and vertical aligned fractures (transverse isotropy with a horizontal symmetry axis or TIH). We establish a quantitative link between fluid saturation and interfacial or fracture compliance and derive simple analytical expressions which link seismic anisotropic measurements to pore and fracture filling fluids. The link between macroscopic parameters such as fracture compliance and physical quantities makes it possible to extract information, such as fluid saturation, from field seismic data. In particular, different behaviors of these parameters may be used to determine whether fractures are dry or saturated. The combined P-and PS-wave AVO analysis can potentially be used to differentiate fluid saturations in Fractures and in shales.