The analysis of the core uncovery and heat-up under low-flow and small break condition is of great importance in assessing severe accident phenomena. Many investigators tried to show up the governing mechanisms about the phenomena, but only a few of them demonstrated the satisfactory informations. In this paper, the System Mean Void Fraction (SMVF) model combined with the drift flux model is developed to predict the transient thermal-hydraulic behavior during core uncovery with or without ECCS flow. The developed model is based on an integral formulation approach, and solved analytically as the closed form solution without involving the quasi-steady assumption. The results have been compared to the existing single tube data with the uniform heat flux and rod bundle experiments with anaxial power profile. Particularly, the comparison with the rod bundle data shows that the developed model predicts more accurate result better than any other previous approaches. Judging from the comparison, the System Mean Void Fraction model is strongly recommended to treat the core uncovery problems. Besides, sensitivity study shows the distribution coefficient of the drift flux model is a very important factor.