The steady flow of isothermal bicomponent coextrusion fiber spinning has been investigated. A model has been chosen in which a Newtonian fluid and a Phan-Thien/Tanner (PTT) fluid were considered to be the core and the skin layer, respectively. This model was adopted to study the effect on spinline velocity of an interaction between two fluids with quite different extensional theology. The effects of the hoop stress, gravity, inertia, and surface and interfacial tensions were disregarded. Only viscous and viscoelastic forces were considered. A uniaxial extension was also assumed as the radius variation in the axial direction is small. The Newtonian fluid has been considered prone to fluctuate during melt processing while the viscoelastic skin layer has a stabilizing effect. The velocity profile was affected by the choice of two characteristic parameters : extensional and shear-thinning parameters, as well as the viscoelastic skin flow rate ratio. Both shear-thinning and extensional parameters play important roles in melt flow. The results show that as the draw ratio increases, the system is dominated by the extensional parameters, whereas slow drawing is dominated by shearing, in spite of the thin viscoelastic skin.