The penetration of elastic surface waves into a solid is inversely proportional to frequency, and this provides an opportunity to nondestructively and easily measure the depth variation of physical properties. Elastic surface wave velocity measurements as a function of frequency should be able to reflect variations with depth of such properties as density, internal stress, hydrogen diffusion in metals, case hardening of steels and so on. One of these, induction hardened steel, has been chosen by us as an example for investigating this problem from an experimental and theoretical point of view. The acoustic impulse technique was used to measure the frequency dependence of the Rayleigh wave velocity on an induction hardened 1043 steel bar. The total change in the velocity for the frequency range 0.5 MHz to 6.0 MHz amounted to over 1% or approximately 10 times the precision of the measurement technique. This dispersion data could be correlated with the depth profile of hardness which ranged from Rc=52 on the surface to Rc=27 at a depth of 0.130 inches (0.33 em). This correlation was substantiated by destructive testing in which the Rayleigh wave velocity was measured at the highest frequency (6 MHz) as a function of the depth by successive removal of 0.03011 (0.0761 em) thick layers. The mathematical problem of converting Rayleigh wave velocity versus frequency data into profiles of physical properties versus depth will be outlined.