In this study, the physical and numerical models are developed to analyze the cooling capability of the passive containment cooling system (PCCS). The PCCS is one of the key passive safety features being developed for the next generation of pressurized water reactors. It is designed to transfer the heat directly from the reactor containment structure to the environment such that the containment design pressure and temperature are not exceeded, and thereby to maintain the containment integrity and minimize the release of radionuclides following any postulated design basis accidents. The functions and several concepts of the PCCS are introduced in this thesis. Also heat transfer mechanisms and applicable correlations are discussed. A numerical scheme is developed to calculate the heat removal rate of the PCCS. The model includes that the heat is firstly convected by condensation of steam through the containment atmosphere to the inner wall of containment sell, and then conducted through the containment wall, and subsequently convected to water film or air flowing along the outer wall of containment shell. To estimate the capability of the PCCS, the heat removal rate is evaluated as a function of the shell surface covered by water film. The developed model is used for the performance assessment of the AP600 PCCS. The calculational result shows that, if the PCCS water is sufficient, the PCCS is capable of effectively cooling the containment following an accident. In addition, sensitivity studies are performed to investigate the effect of containment dimension, noncondensable gas content in containment atmosphere, and the saturation temperature of the steam inside containment.