A recently developed viscous shock-layer method (VSL81) has been applied to predict laminar viscous flows over the windward surface of a shuttle-like vehicle with a perfect gas and an equilibrium air model at high angles-of-attack to simulate reentry conditions. The predictions of wall pressure and heat-transfer data compare well with the limited experimental data available requiring relatively short computing times compared to parabolized Navier-Stokes (PNS) methods. Velocity, pressure and enthalpy profiles are compared at some stations on the body. This method can be used to predict viscous flows over general lifting bodies during reentry. / Master of Science