The seismic anisotropy often detected in the Earth's crust has been attributed in large part to the presence of open microcracks showing some degree of alignment. This alignment is believed to result from the anisotropic state of in situ stress, since any cracks remaining open at depth will tend to be oriented normal to the direction of the minimum in situ stress. Previous workers have calculated the change in elastic wave velocities due to either randomly oriented or perfectly aligned cracks. In this paper the P and S wave anisotropy in the long-wavelength limit is calculated for an arbitrary orientation distribution of cracks. For the case of an orthotropic distribution of circular cracks it is found that a simple relation exists between the P and S wave anisotropy. To test this prediction, ultrasonic P and S wave velocities were measured for propagation in three orthogonal directions through three samples of Berea sandstone as a function of maximum compressive stress applied perpendicular to the bedding plane. The samples were 50-mm cubes and were stressed to peak in a true triaxial loading frame, while the principal stress components parallel to the bedding plane were held constant at 4 MPa. ¿American Geophysical Union 1991