An analytical model for the self-excited vibration of an overflow flexible weir as observed in the French demonstration fast breeder reactor, Super Phenix-1 is proposed. The instability condition was derived for the case in which the plate vibrates at the frequency of the downstream tank sloshing. In this analysis, the flexible plate weir is modeled as a simply supported - free - simply supported - clamped rectangular plate. Eigenfunction expansions were applied for analyzing both plate vibrations and the downstream tank sloshing. The effect of an overflow liquid is formulated based on the assumption that the momentum change due to the collision of an overflow liquid partly transmitted to the pressure rise on the free surface. As a result, the characteristic equation of the system yielding the theoretical stability boundary was obtained. The stability boundary thus derived agreed well with experimental results.