This paper deals with self excited oscillations of the structure coupled with inner fluid occurred in the insulation wail cooling system of fast breeder reactor Super-Phenix-1 (SPX-1) in France during test operations. We analyzed and performed experiments on the instability of multiple cylindrical structure system which has dual flexible weir shells. We measured self excited oscillations changing various parameters such as discharge flow rate, gap of the liquid height between feeding and restitution plenums. In the experiment, it was found out that dual cylindrical shells oscillate in the inverse phase each other with an oval vibration mode under the specific conditions. Comparison between theoretically and experimentally obtained instability region was made, which shows good agreement.