A capillary rheometer with quenching capability was used to study the formation of microstructure in mesophase pitch—a discotic nematic liquid crystal—under the flow conditions of fiber spinning. We report here some observations by reflected polarized‐light micrography on polished sections of specimens quenched during shear and elongational flow, or quenched during relaxation after cessation of flow. A prominent feature of mesophase flow in a capillary is the formation of ‘‘rippled’’ structures that appear to be due to the instability of shear flow in an anisotropic liquid. The ripples display a regular pattern of misorientation from the flow direction. The fully developed microstructures near the capillary exit consist of three microconstituents distributed in a concentric pattern: a fibrous core, surrounded by fine concentric bands with the mesophase layers in zig‐zag radial arrays, and a fine‐textured rim. Upon relaxation, the fine microstructures rapidly decay to disclination arrays, and coarsening continues by disclination‐annihilation reactions. The draw‐down cone, from which a filament is spun, showed no evidence of rippled structures, but instead a tendency to reorient mesophase layers to the axial direction. The rheological memory of mesophase pitch was observed in spinning experiments in which an orthogonal gridlike pattern is imposed by a screen placed above the spinneret. The ripples formed upon passage through the screen dissipate within seconds after flowing past the shear field. In contrast, the orthogonal pattern is much longer lived; its persistence upon reduction to extruded rod or drawn filament is dependent upon the viscosity determined by the spinning temperature.