The sensitivity of the viscoelastic melt spinning process with respect to parameters has not been reported yet in the literature. The study on the sensitivity of the melt spinning process is quite important industrially because it is closely connected with the subject of productivity and product quality of the industrial process. In this study, we investigated sensitivity of the viscoelastic melt spinning process with respect to the velocity and temperature of the quench air, fiber length and the fluid characteristic relaxation time. Maxwell-Oldroyd model is used to describe the rheology of the polymeric materials. It has been found that the quality of the final product depends on the values of the parameters. Further, we have found that it is not possible to change the parameters arbitrary because it may yield irregular fiber or induce breakage of the individual filaments of the spinline. Key Words: Fiber Spinning / Sensitivity / Maxwell-Oldroyd * ssnp@maths.cmb.ac.lk industrial processes the take-up speed is about 50m/s and the extrusion speed is about 10m/s, see [2]. Hence the filament is stretched considerably in length and therefore it decreases in diameter. The ambient atmosphere temperature is below the polymer solidification temperature such that the polymer is cooled and solidifies before the take-up, see Figure 1. In industrial processes a whole bundle of hundreds of single filaments is extruded and spun in parallel, however for the analysis we consider a single filament. The dynamics of melt spinning processes has been studied by many research groups through-out the world during the last decades starting with early works of Kase [5] and Ziabicki [10]. In later works, the energy balance for the heat transfer was introduced into the model, and more and more sophisticated descriptions, including material effects, Fig. 1. Sketch of the melt spinning process.