Abstract: Under severe accident in sodium-cooled fast reactor (SFR), molten corium may fall into the coolant and cause molten fuel-coolant interaction (MFCI). The molten corium is fragmented and solidified to produce debris during MFCI. The debris is relocated on the core catcher or lower head to form core debris bed. The coolability and recriticality of core debris bed are significantly affected by the fragmentation characteristics of molten corium jet. Based on the linear stability theory, kinematic equations and modified Laplace’s law at the contact interface, the growth of surface disturbance of molten corium jet was derived to consider the effect of boiling and solidification behavior. The fragmentation model of molten corium jet was established. Then the criteria for fragmentation of molten corium jet under typical conditions were acquired. The model developed considers the effects of three factors: the relative velocity between melt and sodium, sodium boiling and melt solidification. Among them, the relative velocity is reflected by the classical K-H instability, and sodium boiling and melt solidification are reflected by the impact pressure coefficient Cpb and bending stiffness Ds. Furthermore, the proposed model was compared with COSA experiment results. For the three molten aluminum experiments under non-boiling conditions, when Ds is around 2.0×10^-3 N·m, the predicted mass median diameter (DMM) are in good agreement with the experimental values of test Al-1 and test Al-4. While the experimental results of Al-2 are in good agreement with the results of model with Ds at 1.0×10^-2N·m because the initial temperature of aluminum is lower and the solidified layer is thicker. For the two stainless steel experiments under boiling conditions, when Cpb is in the range of 106-108 Pa·m^-1 and Ds is in the range of 10^-5-10^-6 N·m, the predicted DMMs are in good agreement with the experimental values. Since sodium is an opaque medium, it is difficult to obtain the visualization results of jet fragmentation, such as the thickness of solidified layer (which can be used to calculate Ds) and the interface disturbance amplitude (which can be used to calculate Cpb) during the fragmentation process. In the follow-up, the key parameters of the fragmentation process can be obtained by numerical simulation method (such as MPS). Then the model can be revised and improved in detail. The research in this work not only provides a reliable tool for the evaluation of severe accident but also offers important guiding significance and reference value for design of mitigation measurements of SFR.