A method for reducing the vibration of a rotating cylindrical tank with elastic supports is studied by considering the case where a stationary circumferential flow relative to the tank is created by inserting rotating ring plates whose rotational speed differs from the tank's rotational speed. It is shown that the vibration can be reduced when the flow's relative velocity is negative. The relative velocity appears not only in the inertial and Coriolis terms of the Navier-Stokes equations but also in the dynamic boundary condition on the liquid surface. It is found that the vibration reduction can be caused by the relative velocity that appears in the dynamic boundary condition on the liquid surface. A semianalytical method is presented for the viscous rotating sloshing problem, for which it is customary to resort to numerical methods. The method is verified by comparing with earlier results available for the case with no stationary circumferential flow relative to the tank. This method transforms the viscous rotating sloshing problem into only several ten ordinary differential equations, thereby reducing computational efforts significantly.