Computations are reported of the combusting flows within a hydrogen fuelled model supersonic combustion ramjet (scramjet) operating in a shock tunnel flow. The work is in support of future launches in the HyShot free flight scramjet program. The scramjet simulates all features of a free flight scramjet including inlet compression ramps, combustion chamber and thrust surfaces. The device employs ramp injection and its ignition is thought to be shock induced. The purpose of the investigation is to enhance understanding of the detailed processes which operate within the device. The computational results are compared with pressure measurements for cases of no fuel injection and fuel injection into nitrogen and air coflows. Significant combustion pressure rise has been observed in the latter experiment. The comparison shows that the computations are physically sound and quite accurately predict many features of the flows. However, they fail to predict significant combustion in the fuel + air flow. Detailed examination is made of the computed solution from which it is inferred that the temperatures within the flow are too low for combustion. Therefore, unless the real flows are quite unlike the prediction, combustion would not be expected within them. No convincing explanation for this disparity between experiment and theory has yet been found and investigation is continuing.