On the numerical simulation of transient elastic wave propagation, a heterogeneous finite difference formulation is utilized to study the steel ball impact induced transient diffracted wave fields of a plate with and without crack or flaws. The snapshots of the transient elastic wave propagation will be presented. In the second part, newly developed method for the determination of concrete elastic constants is introduced. The method is based on the measurements of the Rayleigh wave and the skimming longitudinal wave velocities. Instead of detecting the wave displacement normal to the specimen surface, the tangential displacement signal is detected through the utilization of home-made PZT conical transducers. The experimental results as well as the wave characteristics of the impact induced elastic wave will be shown and discussed. Finally, method for the detection of surface breaking crack in concrete will also be addressed.