A study is made of the flow and the shape of the free surface of a non-Newtonian fluid contained in a flat-bottomed cylindrical vessel performing torsional oscillations of small amplitude. For the case where the fluid depth is small compared with the vessel radius, the solution is shown to have a simple radial dependence except in a boundary-layer region near the side wall. It is shown that under certain circumstances the mean steady second-order components of both free surface curvature and radial–axial flow may be in the reverse direction to those for a Newtonian fluid. It is found that flow reversal may occur at any frequency of oscillation, but that surface curvature reversal cannot occur at low frequencies.