Abstract. In the present study, attempts are made to study the behavior of a viscoelastic uid in the hollow ber membrane production process. For this purpose, the uid is considered to obey the Giesekus' model and ow is taken as steady, two-dimensional and isothermal one. The ow eld is obtained using DEVSS/SUPG scheme combined with a free surface tracking method. The obtained results are compared to the case of Newtonian uid. It is shown that the extrudate swell is 20% more in the case of viscoelastic uid. Moreover, the elastic behavior of the viscoelastic uid signi cantly a ects the velocity eld in the extrudate outside the die. It causes the uid ow to become reversed in the middle part of the extrudate as the direct result of the stress relaxation process, whereas such a behavior is not seen for Newtonian uid. Also, the First Normal Stress Di erence (FNSD) distribution in the extrudate is obtained and its variation is discussed. Furthermore, the e ects of operational parameters, including die back pressure and take-up velocity, are investigated. Finally, the predicted extrudate swell for various operation conditions is compared to experimental results showing good agreement between experimental and simulated data.