Ultrasonic waves are highly sensitive to microstructural variations in materials and have been used extensively to investigate anharmonic effects in various metals and alloys[1–3]. A major focus of these studies is on the higher order elastic constants and their relation to the microstructure of the material. Ultrasonic techniques have also proven quite useful for characterizing the stress state of a material [4–6]. Recently, while using the magnetoacoustic (MAC) method to investigate the residual stress in various steel samples, a time dependent change in the results was observed. It became apparent that the measurements were exhibiting anelastic effects due to some intrinsic properties of the samples.