The melt viscosity of narrow distribution, linear, random copolymers of butadiene (75%) and styrene (25%) prepared by anionic polymerization was investigated in both the Newtonian and non‐Newtonian regimes of flow. The Newtonian viscosity is shown to obey the usual 3.4th power dependence onMwThe temperature dependence is represented satisfactorily by the Vogel equation, as modified by Berry and Fox. Non‐Newtonian viscosities are reduced to a single master curve for all polymers, temperatures, and shear rates, using the Newtonian viscosity as the sole shift factor (η/η0vs.η0γ̇). Comparison of this master curve with those of two narrow distribution polybutadienes of different microstructure produces agreement within 0.2 of a logarithmic unit on theη0γ̇‐scale. All three master curves lie one to two decades toward higher reduced shear rates than various “universal” curves reported in the literature for polymers of broader molecular weight distribution.