A rheological interpretation is given for the formation of shaped fibers whose cross section is different from the spinnerette shape. For the study, a rectangular die having an aspect ratio of 6 was constructed, with dimensions 0.1 in. by 0.6 in. Measurements were then taken of the distributions of wall normal stresses at two adjacent walls of the rectangular duct. The measurements show the nonuniform distributions of wall normal stresses over the long and short sides of the rectangle, which is in accord with the nonuniform distributions of extrudate swell on both sides of the rectangle. Explanations are then given for the observed fact that extrudate swell is more pronounced at the long side than at the short side.