Detailed flowfield results have been obtained for sphere-cone shaped bodies at various angles of attack with a 3D nonequilibrium viscous-shock-layer (VSL) code. Recently obtained surface and shock-slip boundary conditions are implemented to account for the low-density effects. These boundary conditions may also be employed with the Navier-Stokes equations with or without a shock-fitting solution technique. A method is suggested for obtaining the input shock shape for the 3D nonequilibrium viscous flow. This approach gives a superior convergence of results, especially under the low-density flow conditions and makes the VSL method self-starting. The analytic algebraic grid implemented with the equations does not add any numerical dissipation. Obtained results show the effect of low density on the surrounding flowfield and surface quantities for a hypervelocity vehicle. Good agreement is obtained with the available numerical results (including the Direct Simulation Monte-Carlo predictions) and experimental data for the low-density flight conditions. Keywords: Axisymmetric hypervelocity vehicles; Three-dimensional flow; Low density flow fields; Viscous shock layer equations; Nonequilibrium viscous flow; Angle of attack. (EDC).