This paper presents a quantitative analysis and a calculation of the mathematic models of the missile in complete movement and the target in its encounter moment by using the information of the control and guide system of ground - to - air missile and the information of the missile in itself, and simultaneously finds out the optimum detonating delay time. On the basis of this, the paper also discusses the problem how to obtain the optimum detonating azimuth of directional warhead and makes an analysis of the simulation result.