The present study deals with the unsteady characteristics of flow concerning flow-induced vibration due to fluid discharge over a flexible cylindrical weir, which occurred in the French demonstration fast breeder reactor, Super Phenix-1. The theoretical analysis of sloshing in a double cylindrical vessel and the drop of the free surface at the fall-in section and the numerical analysis of the inner flow were carried out. In the numerical analysis, unsteady and 2D inner flow with periodic vortex formation and shedding were simulated using the boundary element method and the discreet vortex method. As a result, it was obtained that the frequency of simulated unsteady flow was in good agreement with the natural frequency of sloshing, and the value of frequency converted into the case of the 1/5-scale test model of the Japanese demonstration FBR was about 6 Hz, which is near the frequency of the fluid elastic mode of unstable vibrations.