Long and slender body, like a fuel rod, oscillating in axial flow can be unstabilized even by the small cross flow which can be activated by the flow mixer or turbulent generator. It is important to include these effects of flow disturbance in dynamic stability analysis of nuclear fuel rod. This work shows how eigen frequency of a multi-span fuel rod can be changed by the swirl flow, which is discretely generated by a flow mixer. By solving a state-space form of the eigenvalue equation for a multi-span fuel rod system, the critical velocity at which a fuel rod becomes unstable was calculated. Based on the simulation results, we evaluated how stability of a multi-spanned nuclear fuel rod with mixing vanes can be affected by the coolant flow in an operating reactor core.