The main passive safety system of the Molten Salt Fast Reactor (MSFR) is a cold plug, placed in the bottom of the reactor. In case of an uncontrolled temperature rise in the reactor core, this plug melts, allowing the draining of the molten fuel salt towards a safe configuration. In the present paper, the main physical phenomena occurring in the MSFR during the draining process is presented. Then, a physical model for simulating the draining process is introduced. This model is then used for analyzing different draining scenarios. Finally, the velocity and temperature fields obtained for this scenarios are analyzed in the light of safety considerations.