Abstract: In severe accident situations, the heat transfer of lower head plays an important role in the integrity of the reactor pressure vessel (RPV). This process is very complex, comprising porous debris conduction, heat conduction of RPV wall and the pressure vessel wall and the natural convection of corium. In this paper, a code named FEMOC was made using the finite element method to solve the two-dimensional transient two-phase heat transfer of the lower head. The phase changing process was treated using solid phase increment method, and solidification rate was added into heat conduction equation to measure the solidification of corium. When the material in the element was in two-phase condition, effective heat transfer efficient was used to simulate the real conduction process. Results were compared with results of the SCDAP/RELAP5 calculations. It shows that the model accuracy meets the requirements.