The freeze plug is a key safety component of the molten salt fast reactor (MSFR), one of six next-generation nuclear reactor technologies being developed under the Generation IV International Forum (GIF). It should be designed to melt if an accident occurs, allowing the MSFR to drain before it incurs structural damage. Two freeze plug concepts have been considered in recent years, in which the plug is melted either through the decay heat produced in the core, or through heat generated by special heating rings and stored in steel blocks adjacent to the freeze plug. Variations consisting of both a single freeze plug, and multiple smaller plugs contained in a metal plate, have been proposed. This work seeks to evaluate the feasibility of these designs and study how parameters such as the sub-cooling of the plug affect melting times. Additionally, an alternative, wedge-shaped freeze plug design is proposed for increased reliability.  Simulations performed in COMSOL showed that the decay heat plug melts within 600 s only if placed within 0.01 m of the mixed core flow. Because such a placement makes the plug vulnerable to temperature and velocity fluctuations in the core during regular operation of the reactor, this design is considered unfeasible and is not recommended for further study. On the other hand, melting times under 600 s were possible with the heating ring design for a range of sub-cooling amounts and plug configurations, suggesting that this design is promising. A thin frozen layer was shown to form on top of the metal grate in the multi-plug configurations, preventing heat transfer through the top of the plate. Although the melting behavior of this layer warrants further investigation, its insulating effect was found to generally cause the single-plug designs to melt faster than the multi-plug designs. A simplified, isothermal model of the wedge-shaped plug was simulated using the enthalpy-porosity approach to account for convection. To model the sinking of the wedge, an extended Darcy term approach was developed based on an analytical solution which was validated experimentally, with good agreement. This model shows that melting of the wedge is unsteady, and that melting times depend linearly on the wedge angle and sub-cooling. Unfortunately, melting times of the wedge plug could not be estimated with realistic, non-isothermal, time-dependent boundary conditions. For future study, a customizable numerical solver such as OpenFOAM is recommended, which would allow the sinking of the solid phase to be modeled more robustly through an immersed boundary method.