Abstract: In this artical a unsteady nature of divergent detonation wave has been briefly describees with the assumption of instantaneous steady detonation. In the method for numerical modeling of divergent detonation we have improved artificial stickiness and described ignition process of explosive with cochran's reaction rate and JWL equation of state. A few of typal divergent detonation problems have been Calculated with our 2DL program and Some satisfactory results have been been gotten.