Axial self-excited vibration may be induced in a rocket turbopump by fluid with a tangential velocity component that flows into orifices of balance piston. To avoid such vibration, knowledge of the dynamic characteristics of fluid force induced by swirling leakage flow is required. In this research, the effect of axial rotation and swirl strength on the added fluid force coefficients is investigated by modeling the piston orifice as the combination of rotational and stationary disks, and deriving the unsteady fluid force generated by swirling leakage flow between the disks. As a result, in the case of a parallel flow path, with increasing swirl strength, the added mass and damping increase and the added stiffness decreases. The effect of rotation on the added fluid force coefficients depends on swirl strength. The effect of swirl strength and rotation on the added fluid force coefficients depends on the shape of the flow path.