The molten salt reactor (MSR) is a generation IV reactor with liquid fuel having nearly zero excess reactivity. Due to the very low excess reactivity, it requires a small number of control rods worth to shut down the reactor. However, as it operates at high temperatures, the core reactivity increases as the fuel temperature cools down during shutdown. In such a case, the control rods might not be able to keep the reactor at a subcritical state, and consequently, the fuel must be removed from the core for long-term shutdown into a fuel drain tank (FDT) below the core. This paper is intended to assess the shutdown capability of the first active shutdown system and fuel drain tank of ThorCon MSR by doing neutronic calculations with MCNP6. The results indicated that the control rods having reactivity worth -1.699 %dk/k are unable to maintain the core at a subcritical state as the core excess reactivity increases to +7.760 %dk/k when the fuel reaches room temperature. Therefore, the fuel must be drained to FDT to be cooled down and kept subcritical. Evaluation for various cases of FDT produced the highest multiplication factor of 0.57008 ± 0.00004 at the most conservative condition. The multiplication factor is well below the critical state of 1.0. The evaluations suggest that soon after the control rods shut the reactor down, the fuel has to be drained to FDT to maintain shutdown condition and dissipate the decay heat.