Predictions of two- and three-dimensional, Mach 8 shock-wave/turbulent boundary-layer interactions with a Navier-Stokes solver are presented. A k - l two-equation turbulence model is used in the calculations. The two-dimensional cases are shock impingements generated by 5- and 10-deg wedges on a well-developed turbulent boundary layer. The three-dimensional case is a crossing shock flow generated by two symmetric 15-deg wedges. Results are compared to experimental surface pressure and heat transfer data and show good agreement. The importance of a compressibility correction to the turbulent length-scale equation is demonstrated. The Navier-Stokes solver uses an upwind discretization of the convective fluxes. The code uses a planar relaxation solver and includes implicit viscous and turbulence source terms. The turbulence model and Navier-Stokes equations are fully coupled in the flow solver.