A longitudinal micromovement of ultrasonic frequency, in the same direction as the mean flow velocity, is applied to the walls of Couette and Poiseuille flows. The constitutive equations considered are those for Newtonian or Bingham models in the bulk, adherence or linear slip at the wall. This micromovement is shown to have a strong influence on the flow properties due to the existence of the yield stress in viscoplastic materials. The key parameters of the problem are the Oldroyd (Od) or Bingham (Bn) numbers. The dimensionless velocity of vibrations U-0, and the vibrational Reynolds number Omega(0) also play an important part. For large Od values, velocity-driven plane (Couette) flows may display significant reductions in stress, even when neglecting vibrational inertia (Omega(0)) much less than 1). In contrast, for pressure-driven (Poiseuille) flows in circular tubes, vibrational inertia has to be taken into account so that the movement transmitted to the fluid is different from a rigid block displacement, and a mean flow rate increase is obtained, the range of which depends on the value of Bn. Indications are given on the way slip at the wall, or shear-thinning viscous behavior modify these results. In order to check these effects, at least in part, the experiments were carried out using extrusion flows with high-power ultrasound applied to a circular die and several raw elastomers in two cases: flows with a constant mean flow rate, and the more complex case of flows created by a screw of zero compression ratio rotating at a given speed. In the second case, an instantaneous decrease in pressure is observed, as well as a simultaneous increase in flow rate. Whatever the case, a new stable regime may be reached after a while, and significant decreases in pressure drop are observed when vibrations are applied with rubber compounds, which may be described as yield stress fluids. These variations cannot be explained solely by the increase in temperature of the extrudate, and they compare well with the theory developed.