The study of elastic properties of fractured/cracked rocks has been an important subject of interest in seismology and geophysical exploration. Downhole logging provides a direct measurement of fractured rock properties in terms of elastic wave velocities and anisotropy. Most existing studies only provide qualitative descriptions of fracture properties as evidenced from the acquired measurements. To better use downhole measurements, we have derived a comprehensive theoretical analysis and developed an inversion technique to characterize fracture properties. Theoretical results for cracked rocks show that crack density, crack alignment direction, and crack filling materials are the three main fracture parameters that strongly affect the elastic wave properties of fractured rocks. Furthermore, a detailed analysis of the crack effects on elastic properties shows that the measured elastic moduli can be used to evaluate the crack parameters of cracked rocks. We assume that cracks with any orientational distribution can be divided into two parts: horizontal and vertical. Based on the theoretical analysis, we develop an inversion method to estimate fracture parameters from well logs acquired in a vertical borehole. We assume a rock-physics model for rocks that adds effective horizontal and vertical cracks that are filled with liquid in an isotropic background, the elastic and fluid properties of which are inverted from the measured logs. The inversion method enables the quantification of the directional crack density and crack-filling material when applied to field logging measurements acquired in fractured formations. Theoretically predicted fracture properties are validated with formation microresistivity scan logging data and are consistent with the interpretation results.