In-line rheological measurements of a polymer melt were investigated in steady tube flow using a combination of velocity and pressure drop measurements. In tube flow, the fluid experiences shear rates that theoretically range from zero at the centre to a maximum at the wall. For complex fluids, this implies that the fluid will exhibit a wide range of viscosities that vary across the tube. Hence, from a single velocity profile in a fully developed tube flow and a simultaneous pressure drop measurement, the shear viscosity as a function of shear rate can be calculated. This point-wise rheometrical technique was pioneered in our laboratory using magnetic resonance imaging to measure the velocity profiles. In the present study, ultrasonic velocimetry is used to measure the velocity profiles. Experimental results with a polydimethylsiloxane melt showed that the shear viscosity can be measured over nearly one and one-half decades of shear rate, 1.6–17 s−1, from a single velocity profile. Over this range of shear rates, the shear viscosity decreased from 113 Pa s to 102.6 Pa s. These are the first measurements of shear viscosity of a polymer melt by this technique. The shear viscosity as measured with a cone and plate rheometer compared favourably with the viscosities determined using point-wise rheometry in the same shear rate range.