By considering the constitution relationship between stress and strain in viscous EDA media in the domain of frequency, seismic wave equations in the media in the domain of time and space are established. The anelastic effects induced by cracks or fractures are shown by the third derivatives of displacement components with respect to time in the equations. After solving the equations for the seismic propagation of plane waves, seismic velocity, attenuation and quality factor ( Q value) are obtained, and their azimuthal anisotropy in the dry cracked and water saturated cracked EDA media are studied. The results show that, seismic velocity, attenuation, quality factor ( Q value), especially attenuation or quality factor ratio of 2 kinds of qS wave can be used to indicate the existence of oriented cracks and material contents in the crack. Meanwhile, elasticity is predominant at low frequency, and anelasticity is significant at high frequency. By considering the constitution relationship between stress and strain in viscous EDA media in the domain of frequency, seismic wave equations in the media in the domain of time and space are established. The anelastic effects induced by cracks or fractures are shown by the third derivatives of displacement components with respect to time in the equations. After solving the equations for the seismic propagation of plane waves, seismic velocity, attenuation and quality factor (Q value) are obtained, and their azimuthal anisotropy in the dry cracked and water saturated cracked EDA media are studied. The results show that, seismic velocity, attenuation, quality factor (Q value), especially attenuation or quality factor ratio of 2 kinds of qS wave can be used to indicate the existence of oriented cracks and material contents in the crack , elasticity is predominant at low frequency, and anelasticity is significant at high frequency.