Based on rheological experiments with a cellulose solution in N-methylmorpholine-N-oxide (NMMO), it was found that the shearing stress generated in the flowing viscoelastic fluid decreases with an l/d ratio in a rheometer capillary. This reduces the elastic response and the outflow of the fluid becomes more uniform. At constant temperature, the elongational viscosity of the solidified stream of the cellulose solution in NMMO is reduced with increase of the deformation rate, which makes it possible to increase the fiber-formation velocity within the air zone.