Rheological measurements are reported of the behavior of a normally stiff paste of fine iron ore and 16% (w/w) water, flowing in a tube which was mechanically vibrated. The ranges of cyclic frequency and peak‐to‐peak amplitude were 15–30 Hz, and 0.508–1.27 mm, respectively. As is known, mechanical vibrations have the ability to “liquefy” pastes and in the present case the liquefied paste flowed through the tube under a very modest pressure head. The deductions that could be made depended on the assumptions, for on the one hand, if no slip was assumed to exist at the tube wall, then the calculated viscosity at any tube diameter could be correlated with the peak cyclic acceleration, viz.,Aω2,whereAis the peak‐to‐peak amplitude and ω is the angular frequency. On the other hand, if slip at the wall was assumed, then the inference had to be made that the flow was more in the nature of rod flow, although the results were puzzling. While it is possible in principle to deduce, from suitable measurements, the relative values of the rheological parameters in slip flow of a Bingham fluid, in the present case this was not possible. Neither was it considered wise to use rheological measurements made earlier on a different apparatus, viz. the squeeze‐flow one, and that reported by Deysarkar and Turner elsewhere. In fact the work reported herein demonstrates that different apparatuses show different behavior. This possibly arises from the physical processes by which the mechanical vibrations of each apparatus were imparted to and transmitted in the paste.