Acoustic microscopy can be used for very localized measurements of the velocity and attenuation of surface waves, and hence is a possible technique for nondestructive evaluation of near surface damage due to fatigue, machining, friction, wear, etc. Because the frequency of operation of an acoustic microscope is high, usually above 100 MHz, the wavelength of the surface wave is relatively small, and thus the roughness of the specimen may affect the wave velocity. In most cases the specimens must be polished to a metallurgical level to ensure that the true Rayleigh wave velocity, i.e., the one for a smooth surface will be measured. For some cases the specimens should, however, not be polished. For example, for the prediction of fatigue life, the roughness may increase during the fatigue test. Usually there remains a certain amount of roughness on the surface after friction, wear or machining. Polishing or any other surface preparation process may destroy the true surface condition of the specimen. Therefore, measurements should often be made for specimens with rough surfaces and it is then important to know the effect of surface roughness on the surface wave velocity in order that roughness effects can be distinguished from the effects that are of actual interest in the measurement.