In order to develop nondestructive techniques for the quantitative estimation of creep damage a series of crept copper samples were prepared and their ultrasonic velocities were measured. Velocities measured in three directions with respect to the loading axis decreased nonlinearly and their anisotropy increased as a function of creep-induced porosity. A progressive damage model was described to explain the void-velocity relationship, including the anisotropy. The comparison of modeling study showed that the creep voids evolved from sphere toward flat oblate spheroid with its minor axis aligned along the stress direction. This model allowed us to determine the average aspect ratio of voids for a given porosity content. A novel technique, the back propagation neural network (BPNN), was applied for estimating the porosity content due to the creep damage. The measured velocities were used to train the BP classifier, and its accuracy was tested on another set of creep samples containing 0 to 0.7 % void content. When the void aspect ratio was used as input parameter together with the velocity data, the NN algorithm provided much better estimation of void content.