In this paper, we apply the transient elastic waves to the nondestructive evaluation of elastic constants and crack depth in concrete specimens. We determined the elastic constants of a concrete specimen through the measurements of the Rayleigh and the longitudinal wave velocities. Furthermore, transient elastic wave experiment on a concrete block with a normal surface-breaking crack is conducted. The measured diffracted wave signal from the crack is in agreement with the simulated signal calculated from a 3-D finite difference program. Finally, we demonstrated that the depth of the normal surface-breaking crack can be determined with an optimization algorithm.