During the past decade or so there have been significant advances in the mathematical modeling of nondestructive testing (NDT) techniques. The current state of modeling is reviewed, with the aim of demonstrating the important role that it can play in improving and validating NDT techniques and procedures. This paper was presented at the 6th International Offshore Mechanics and Arctic Engineering Symposium, (1987). Since that time, a number of advances have been made in mathematical modeling. A more recent review of mathematical modeling techniques, with additional references, is currently in preparation by the authors.