It is very important and necessary to know the critical range (the range at which collision is unavoidable) for collision avoidance by course changing maneuver. In order to obtain the critical range by course changing, it has been found necessary to develop a mathematical model of collision avoidance and occurrence. We have used a new analytical technique, using an area of collision target's position. And different versions of the critical range by course changing are obtained under assumptions such as a) one ship evades, while the other stand on. b) one ship evades while being pursued by the other. The study shows that the critical range by course changing depends strongly on the two ship's speed difference, and on the permissible maneuver.