Even before Fukushima accident occurred, the safety authorities have required that new power plant designs must take into account beyond design-basis accidents including possible core meltdown. Among the mitigation strategies, the corium retention must be ensured, so a core catcher is implemented in the design of the Generation IV Sodium-cooled Fast Reactor. An internal core catcher within the vessel (in-vessel retention) is the option chosen for the European Sodium-cooled Fast Reactor investigated in the H2020 ESFR-SMART project. The new core investigated in ESFR SMART with lower void effect has a better behavior in case of severe accident. The use of passive control rods is also an improvement for prevention of severe accident. Moreover, we have in the ESFR SMART core dedicated tubes for corium discharge that should allow discharging quickly the melted materials and should help to prevent large criticality. Calculations show that after several seconds, these discharge tubes begin to open, and the corium arrives by this preferential way on the core catcher, quicker and in limited quantities at the beginning of the accident. However, the core catcher is designed to be able to retain the whole core meltdown. Its design allows good possibilities of cooling by natural convection of sodium. Some thermal calculations were provided with a multi-layer concept but the global mechanical conception seems difficult. So a one layer core catcher in molybdenum, material compatible with sodium and used on the core catcher of the last SFR, started in 2016: BN 800, is investigated. Explanations are given on the choice of this material proposed for the catcher and used for thermal calculations. With the proposed design, the corium is spread on the core catcher and the residual power of the corium can be dispelled by natural convection by the sodium circulating around and above the core catcher without boiling of sodium if the melted core is less than about 25% of whole core. In case of bigger quantities of melted core, boiling of sodium could appear under the core catcher. Further less conservative calculations would be necessary to better know the limit.