Abstract: The best estimate system analysis code RELAP5 was used to analyze the natural circulation systems. The instability boundaries of one natural circulation system were obtained under different conditions. According to present results, most of the boundary points were found in the low subcooled boiling zone. The natural circulation systems can tolerate high subcooled boiling, and the disturbance of bubbles departing from the wall and condensing in the subcooled boiling region may be the inherent source to induce the instability, then the flow oscillations can become self-sustained and evolve because of the phase differences among system driving force, resistance and flow rate.