Abstract: The wave velocities of whole rock samples in triaxial experiments under different stress paths, and the wave velocities of rock samples with saw cut in uniaxial experiments were measured by ultrasonic impulse method. It is shown that the stress path and the presence of faults are two possible factors influencing the anomaly of wave velocities. The first one is concerned in time and space, while the second one is concerned in space only. It is also shown that for correct evaluation of the significance of the anomaly of wave velocities in earthquake prediction, people must do their best to take into account every kind of factor influencing the anomaly of wave velocities.