The flow of a time-independent fluid through a vibrated tube is studied both numerically by CFD simulation and experimentally. The effects are studied for Newtonian and non-Newtonian fluids which obey Bingham plastic, power-law or Herschel-Bulkley behaviour. The superimposed mechanical oscillations have no effect on the flow of Newtonian fluids, bur can greatly influence that of shear-dependent fluids. Flow enhancement is obtained with shear-thinning fluids whereas flow reduction occurs when a shear-thickening fluid is vibrated. The effects of the various theological parameters are investigated, and the flow behaviour index emerges as the most influential. The enhancement is a function of both vibration frequency and amplitude, but the same enhancement is generated with different amplitude-frequency combinations that correspond to the same peak acceleration. The CFD predictions are in both qualitative and quantitative agreement with experimental measurements.