An investigation of the interaction of shock waves with bodies moving at supersonic speeds was conducted using computational and numerical methods. The investigation characterises the various interaction configuration types and defines a set of interaction type criteria which serve as type transition criteria. An attempt was made to model the shock-moving body interaction experimentally using a diaphragmless double driver helium/air shock tube facility designed for this purpose. The experimental work was abandoned when the chosen experimental method proved unable to generate the wedge Mach numbers and impinging shock strengths required for an investigation of the various interaction type transitions. This work has classified eight new shock-supersonic body interaction types which, are combined with three shock-on-shock interaction types previously identified in computational and experimental work conducted in the 1960’s and’70’s. The previous computational model used linearising approximations and is replaced by a more recent computational model which has been adapted to meet the requirements of the current work. The three shock-on-shock interaction types were reclassified to fit in with the new computational model. The new computational model considers both head-on and oblique interactions and the eleven interaction types were characterised and various transition criteria identified using parts this model. The interaction types and transition criteria were then confirmed numerically by applying an arbitrary Lagrangian Eulerian finite volume scheme on unstructured adaptive meshes with moving boundaries, developed by a PhD student at the School of Mechanical, Industrial and Aeronautical Engineering at the University of the Witwatersrand. The investigation has shown that the choice of reference frame affects the Mach number of a flow behind a normal shock propagating into a supersonic flow. While the flow is accelerated by the shock, increasing the flow velocity, the Mach number of the shock can increase or decrease depending on the strength of the impinging shock and wedge Mach number. The eleven interaction types comprise the the three old shock-on-shock interaction types, a new irregular shock-on-shock interaction type, two expansive interaction types, three detached shock interaction types and two overtaking interaction types. Of the three shock-detached bow shock interactions iii