The shear dependence of viscosity of benzene solutions of natural rubber was studied at rates of shear from about 500 down to less than 1 sec.−1. Measurements involved following the change of pressure head with time of the various solutions flowing in a capillary, U-tube viscometer. Curvature in the plots of the logarithm of pressure head versus time indicated non-Newtonian flow. From such curves, reduced viscosity data over the above-mentioned shear range were readily derived. As a check, data over the range 100–500 sec.−1 were also obtained with a five-bulb viscometer of the Krigbaum–Flory type, and these data overlapped those obtained with the U tube. The reduced viscosity increased very sharply with decrease in gradient, making extrapolation to the viscosity axis quite unreliable. However, a theoretical relation proposed by Bueche fitted the composite data rather well. This work furnished a nice technique for determining the zero shear reduced viscosity (ηap/c)0 without the necessity of performing an uncertain extrapolation: evaluate the parameters of the Bueche formula which best satisfies the experimental data over a fairly wide range of shear rates, and then calculate (ηap/c)0 directly.