Thin-layer Navier–Stokes solutions are obtained for an incompressible laminar flow over a hemisphere–cylinder at 10°, 30° and 50° incidence to exhibit some three-dimensional separated flow characteristics. Some of the results are compared with a previous water-tunnel investigation for the same body geometry. Good agreement is found, even for some detailed features. Although the geometry is relatively simple, the separated flow surprisingly embraces a number of intricate structural characteristics unique to three-dimensional flows. Particularly noteworthy are the separation sequence at increasing incidence, tornado-like vortices, outward-spiralling vortices, limit cycles, coaxial counter-spiralling patterns and horseshoe vortex systems. Physical insights to these new features are offered.