A low frequency (0.5 - 2.5 Mhz) acoustic microscope is used to generate and detect surface waves in isotropic and anisotropic solids. In this microscope one transducer with a cylindrical concave front face produces a line focused ultrasonic beam which strikes the specimen at any desired angle. The reflected beam is received by another transducer. When the incident angle of the striking beam becomes equal to the critical angle of the reflector, surface waves are generated otherwise the beam is specularly reflected without generating any surface wave. It is shown in this paper that by measuring the change in the arrival time as the distance between the reflecting surface and the transducer changes one can predict if the surface waves have been generated or not. Experiments are carried out with copper and aluminum blocks and graphite-epoxy (graphite fibers in epoxy matrix) composite plate. It is found that it is easier to generate and detect surface waves in isotropic metallic blocks where Rayleigh waves are nondispersive than anisotropic graphite epoxy composite plate where Lamb waves are dispersive.