Despite the modeling capabilities of current computational fluid dynamics (CFD), there still exist problems and inconsistencies in simulating fluid flow in certain flow regimes. Most difficult are the high-speed transonic, supersonic and hypersonic wall-bounded turbulent flows with small or massive regions of separation. To address the problem of the lack of computational accuracy in turbulence modeling, NASA has established the Turbulence Modeling Resource (TMR) website and has issued the NASA 40% Challenge. The aim of this challenge is to identify and improve/develop turbulence and transition models as well as numerical techniques to achieve a 40% reduction in the predictive error in computation of benchmark test cases for turbulent flows. One of the phenomena of considerable interest in the 40% Challenge is the shock-wave boundary layer interaction (SWBLI) that occurs on aircraft surfaces at transonic and supersonic speeds and on space vehicles at hypersonic speeds. The correct modeling of shock-waves is complex enough, but the occurrence of SWBLI adds to the complexity by promoting flow separation, heat transfer, and pressure gradients on the surface. SWBLI may occur in both the external and internal flow path of air and space vehicles; therefore, it is important to accurately predict this phenomenon to improve the design of aircraft and space vehicles. The majority of CFD codes utilize the Reynolds Averaged Navier-Stokes (RANS) equations and employ various turbulence models. The most common among these turbulent models are the one-equation Spalart-Allmaras (SA) model and the two-equation Shear Stress Transport (SST) k-[omega] model. In recent years the CFD community has, in greater number, also started to adopt Large-Eddy Simulation (LES), Direct Numerical Simulation (DNS), and hybrid RANS-LES approaches for improving the accuracy of simulations. However currently, solving the RANS equations with eddy-viscosity turbulence models remains the most commonly used simulation technique in industrial applications. In this research, the one-equation Wray-Agarwal (WA), SA, and SST k-[omega] turbulence models are used to simulate supersonic flows in a 2D compression corner at angles of 8° and 16°, a partial axisymmetric flare of 20°, a full-body conical axisymmetric flare of 20°, and an impinging shock over a flat plate at 6°, 10°, and 14°. The ANSYS Fluent and OpenFOAM flow solvers are employed. Inflow boundary conditions and mesh sensitivity are examined to ensure the grid independence of computed solutions. For each of the three turbulence models, heat transfer, surface pressure, skin friction, and velocity profiles are compared with the available experimental data. It is found that the results from the WA model are in similar or better agreement with the experimental data compared to the SA and SST k-[omega] models for the majority of cases considered.