The aim of this thesis is to design and evaluate a non-destructive evaluation (NDE) system for the inspection of single crystal turbine blades. Turbine blades are the components within jet-engines that convert the hot, high-pressure gas exiting the combustion stage into mechanical power. During operation, these components are highly stressed and are surrounded by extremely high gas temperatures. As such, there is the potential for defects to initiate in-service. One way to ensure the structural integrity of these engine components is by periodically inspecting them for defects. The ability of the inspection to be performed in situ is highly advantageous, as this eliminates the cost and time delay associated with removing the turbine blades from the engine prior to inspection. A 20 ultrasonic phased array system was chosen for this project, as these systems can perform rapid volumetric inspections whilst being portable enough to be used in situ. Modem turbine blades are manufactured from single crystal nickel-based superalloys for the excellent mechanical properties these materials exhibit at elevated temperatures. However, these materials are elastically anisotropic. The propagation of ultrasonic waves through anisotropic materials is far more complex than the isotropic case. This causes significant difficulties when inspecting anisotropic single crystal components with ultrasonic arrays. Therefore, analytical models are developed to predict the propagation of ultrasonic waves in anisotropic materials. These models are used to correct an ultrasonic imaging algorithm to account for the anisotropic behaviour. To implement the corrected algorithm effectively, the orientation of the crystal in the component under inspection must be known. Therefore, crystallographic orientation methods using 20 ultrasonic arrays are developed and evaluated. The corrected algorithms and crystallographic orientation methods are used to develop an in situ 20 ultrasonic array inspection for a specific high-pressure single crystal turbine blade. The inspection is designed to detect and size cracking in the root section of the turbine blade. The developed inspection system is fully evaluated in a quantitative manner for its defect detection sensitivity and sizing capability.