This paper contains an investigation of the ability of some of the current turbulence models to predict viscous effects in supersonic Mach number regimes. In most cases, these turbulence models have been derived and validated in traditional subsonic to transonic Mach number regimes and their application to supersonic and hypersonic regimes is assumed valid without a proper recourse to understanding the wider implications of the viscous flow field at high Mach numbers. In such flow regimes, such characteristics as the strong shock interactions with control surfaces and evolving vortices present in the flow, or other large entropy gradient effects brought about by the forebody or other fin surfaces, produce non-trivial challenges for the turbulence models. This study was aimed at interrogating the strength of the turbulence models to model such physics. The Applied Vehicle Technology Panel Group 082 of the Research Technology Organisation selected a dual control NASA missile to investigate the capabilities of Computational Fluid Dynamics (CFD) to predict the flow field and performance characteristics of complex-shaped projectiles at high Mach numbers. There are two types of difficulties that are encountered when computing such problems. The first type are geometry based, and are related to the shape of the nose and forebody, number and types of strakes or forward control mechanisms, fin geometry deployment, and shape and design of the cowls and intakes. The second type of difficulty deals with flow complexities such as the heat transfer (M > 4) implications; the vortices shed from the forebody and other control surfaces; the interaction of these vortices with the body structures, the free stream, and with each other; the base flow interaction with the free stream; the boundary-layer development; and, in the case of supersonic flows, the shock boundary-layer interactions. Air-breathing missiles with intakes or missiles with jet-controlled guidance systems add to the flow complexities. Various turbulence models employed in current CFD codes are tested for their ability to address these viscous issues.