A finite-difference method recently developed to study three-dimensional viscous flow is applied here to the supersonic boundary layer on a sharp cone at moderate angles of incidence (α/θ [les ] 2, angle of attack α, cone half-angle θ). The present analysis differs from previous investigations of this region in that (i) boundary-layer similarity is not assumed, (ii) the system of governing equations incorporates lateral diffusion and centrifugal force effects, and (iii) an improved numerical scheme for three-dimensional viscous flows of the type considered here is used. Solutions are shown to be non-similar at the separation streamline with local shear-layer formation. Detailed flow structure, including surface heat transfer, boundary-layer profiles and thickness, and the formation of swirling pairwise symmetric vortices, associated with cross-flow separation, are obtained. Good agreement is obtained between the present theoretical results and the existing experimental data.