The ultra-high pressure water-jet is a novel means of cutting and cleaning surfaces. In the last two decades, researchers have been studying the characteristics of a water-jet, and tried to control its cutting process. However, existing knowledge about water-jet cutting is still ambiguous. Thus, it cannot satisfy the requirement of precise control. In this paper, linear stability theory is applied to theoretically analyze the relationship of nozzle diameter and wave number in the water flow with the stability of the water-jet. Theoretical conclusions satisfy the experimental results obtained.