An analysis has been made of previously published data and data obtained by the authors. The possibility has been shown of quantitatively describing the stress and velocity fields in the flow of polymer systems through spinneret channels using the photoelasticity method and media of contemporary computer technique. It has been found that the region of lengthwise flow at the inlet to the spinneret channel is the site of action of the maximum stretching stresses, which aid in deformation and orientation of polymer macromolecules along the channel axis. In the regions at the walls, principles of shear flow predominate, wherein the tangential stresses, which are maximum at the edges of the entrance, are diminished as one moves away from the inlet, to values which are characteristic of an established shear flow. The relative length of the channel section in which complete relaxation of normal stresses on the channel axis (L/D ≈1.5–2) is comparable with the length of the spinneret channels which are used in the man-made fibre industry, due to which a residual orientation of the polymer macromolecules at the exit from the spinneret is possible.