Non-destructive inspection is widely used to ensure that engineering structures such as railway rails, bridges, nuclear reactor pressure vessels, offshore oil platforms, airplane airframes and so on contain no unacceptably large defects. Such defects, if they were present in the structures, could cause failure under certain applied loads. Generally, the most serious defects are cracks which occur during manufacture, either in castings or in welds, or during service due to cyclic loads and environmental attack. The non-destructive inspections are carefully designed to be capable of detecting these crack-like defects. I am concerned here only with ultrasonic inspection techniques and consider the recent developments which have taken place in modeling them. Some of the modeling work has been driven by requirements of inspection of pressurized water reactors, some by inspection requirements foreseen for fast reactors. All the developments have application to some aspects of inspection of all reactor types: fast reactors, pressurized water reactors and gas cooled reactors; and indeed to the inspection of many other engineered structures too.