An overview of the mathematical modelling work on NDE as a part of PISC III international activities given. The models consist of a description of ultrasonic probes and the interaction of the sound field with postulated defects. An important objective is to promote the practical application of models as an aid to more effective and efficient inspection procedures and interpretation of results. Comparisons of the approximate solutions with - whenever possible - exact analytic solutions and with careful measurements performed during the paranetric studies shall assess the utility and the accuracy of the models.
