Ultrasonic nondestructive testing has important applications in, for example, the nuclear
power and aerospace industries, where it is used to inspect safety-critical parts for flaws.
For safe and reliable testing, mathematical models of the ultrasonic measurement systems
are invaluable tools. In this thesis such measurement models are developed for the ultrasonic
testing for defects located near non-planar surfaces. The applications in mind are
the testing of nuclear power plant components such as thick-walled pipes with diameter
transitions, pipe connections, etc. The models use solution methods based on frequency
domain boundary integral equation methods, with a focus on analytical approaches for the
defects and regularized boundary element methods for the non-planar surfaces. A major
benefit of the solution methods is the ability to provide accurate results both for low, intermediate
and high frequencies. The solution methods are incorporated into a framework
of transmitting probe models based on prescribing the traction underneath the probe and
receiving probe models based on electromechanical reciprocity. Time traces are obtained
by applying inverse temporal Fourier transforms, and it is also shown how calibration and
effects of material damping can be included in the models