Cu single-crystal cubes have been γ irradiated in the  and [11¯0] directions, and the ultrasonic attenuation due to dislocation damping has been determined in the  direction after the various irradiation treatments. Fricke dosimetry indicates that about 10% less secondary electron energy exits the crystal in the [11¯0] irradiation than in the  irradiation. The fact that more energy is absorbed in the [11¯0] irradiation is consistent with the dislocation damping studies which indicate that more dislocation-pinning point defects are created in this case. The damping data obey the Granato-Lücke damping theory, and quantitative predictions as to the dislocation loop length and number of pinners created during irradiation are made on the basis of the theory. The anisotropy in radiation damage is consistent with theoretical predictions of anisotropy of replacement energy and focusing energy in Cu.