The nondestructive testing and evaluation is commonly used in civil engineering for the evaluation of existing structures and for the quality control in new construction. Various NDT methods have been developed for civil infrastructures. In this paper, NDT methods based on the stress wave propagation such as impact echo, SASW and IE-SASW are introduced. The methods have advantage because the measured wave velocity is directly related with the engineering property of structure such as stiffness. The testing setup and data reduction techniques of various methods are discussed. The factors influencing test result and the advantages/limitations of each method are also reviewed. Time domain, frequency domain, and emerging time-frequency domain analysis techniques are utilized for the better interpretation of test results. The models of slab type structures and deep foundations including various defects and boundary conditions at known locations were made and the applicability of various methods was investigated. Finally, field applications to the concrete member in nuclear power plant containment structure and deep foundation were performed.