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This paper presents the results of measuring the Rayleigh wave as well as longitudinal wave velocities in a concrete specimen using transient elastic waves. The Rayleigh surface wave generated by a steel ball impact on a concrete material is studied in detail and then a method for the determination of Rayleigh surface wave velocity based on the cross-correlation method is proposed. The longitudinal wave velocity of a concrete specimen is determined by measuring the wavefront arrival of a longitudinal wave. A special triggering device for the accurate determination of the impact time origin is utilized.