Experimental and theoretical studies on the air-assist coaxial atomizer have been continuously carried out for a long time. But now the importance of the theoretical study is tending to increase as with the development of computer. This study is concerned to the spray modelization, especially, the instability of the liquid jet surrounded by the air stream which flows with high velocity. To study the phenomena of the break up, we used the linear theory based on the classical Kelvin-Helmholtz theory for capillary wave at a simple interface and we investigated the variation of liquid core radius. As a result, we obtained that the drop diameter and the variation of the liquid core radius predicted by using our model are reasonable.