The rheological equations for steady-state isothermal spinning of polymer melts are solved by assuming the melts to be viscoelastic material. Spinning velocity equations are derived and discussed for the special limiting cases. When the relaxation time of polymer is small compared with the time for filament flow, the velocity equation becomes expontial, but when the imposed stress is large compared with the modulus, the velocity-spinning way relation becomes nearly linear. Simpler relation was also derived and discussed by assuming radial and shear stresses are nogligible compared with the axial stress.