Hollow fibers are considered for a wide range of applications as their inherent internal void geometry enhances functionality and reduces material need. This study examines how stresses in polymer melts affect fiber void space and cross-sectional shapes during 4-C segmented arc melt spinning, a process where polymer extruded through four C-shaped arcs coalesce after extrusion to form a single hollow fiber. We conducted spinning trials under various conditions and analyzed hollow fiber cross sections by measuring circularity and hollowness, defined as the volume fraction of the fiber's hollow core relative to the total fiber volume. Rheological properties of different polypropylene melts at the temperature and conditions of spinning are related to the final fiber properties to show that the processing parameters of spinning temperature and flow rate are of significance. Experiments maintaining constant denier, or linear density, reveal that hollowness and circularity are related to the flow behavior through the Weissenberg number (Wi). At low Wi, hollowness increases with Wi; however, as Wi exceeds unity, the polymer takes on more elastic characteristics and the fiber transitions to constant hollowness, followed by instability at higher Wi values. Computational fluid dynamics (CFD) simulations using the Giesekus model allow for the analysis of stresses present during extrusion, revealing that uneven stress distributions at high Wi lead to a decrease in the circularity of the inside of the fiber. At low Wi, the extruded polymer melt has more viscous character and more time to resolve stresses in the melt before solidification, creating a fiber that retains less hollowness but more shape uniformity. A generalized inverse relationship between fiber circularity and hollowness is also observed across various polymer samples, flow rates, and temperatures. These findings provide valuable insights on hollow fiber spinning and predictions of hollow fiber geometry based on the viscoelastic properties of the polymer melt.