The objective of this research is to study how ultrasonic waves scatter from partially closed cracks and other imperfect interfaces. An important part of this research is developing a model for such interfaces that takes account of surfaces roughness and the partial contact between crack or bond faces. An equally important part is developing a model of the measurement process that accounts for the transmitting and receiving characteristics of the transducers. The results of this research will enable more complete, quantitative information about such cracks and interfaces to be extracted from scattered ultrasonic signals. Examples of such quantitative information include the size of a fatigue crack and an estimate of the strength of a diffusion bond. Such information enables one to assess quantitatively the quality and reliability of manufactured parts. The approach used is interactive. It involves a combination of analytical and numerical approaches whose outcomes will be continuously compared. Moreover, the predictions from these calculations will be continuously compared with existing data from measurements carried out at the Center for Nondestructive Evaluation at Iowa State University.