The 4S (Super-Safe, Small and Simple) reactor is a sodium-cooled fast reactor aiming at an application to dispersed energy source and multi-purpose use. Its electrical output is 10MW or 50MW and the core lifetime can be varied from 10 to 30 years without refueling. An introduction of RVACS (Reactor Vessel Auxiliary Cooling System) can enhance the passive decay heat removal capability. In the present study, the RVACS performance in 4S reactor (10MWe, pool-type) was analytically evaluated under the functional loss of RVACS stack condition, which is considered as a beyond design basis event. A protected loss of heat sink accident was selected and simulated to evaluate the capability of RVACS to cool the plant under such an unusual condition. The three-dimensional thermal hydraulic analysis was conducted by PHOENICS code. Analytical results show that the functional loss of air outlet stack has more effect on RVACS performance than that of air inlet stack. The air flow rate in RVACS under the functional loss of one out of two outlet stacks decreases up to approximately 60% and the heat removal rate approximately 70%, comparing with those under the normal stack condition. However, the maximum hot plenum temperature is low enough to satisfy the safety criteria.