Axial self-excited vibration may be induced in a balance piston by fluid with a tangential velocity component that flows into the piston orifices. To avoid such vibration, knowledge of the dynamic characteristics of axial self-excited vibration induced by swirling leakage flow is required at the design stage. In this research, the effect of axial rotation and swirl strength on the added fluid force coefficients is clarified 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, reduction of the relative velocity in the circumferential direction is shown to destabilize the oscillatory system. In particular, the effect of swirl strength on the fluid force coefficient is found to be larger in the case of the divergent channel than in the case of the parallel flow path.