Abstract: This paper provides a method that surface of transition zone is constructed.The geometric and mathematic solution is given by projecting moving center of sphere with varied radius on the cylinders.A typical surface of transition zone is trajectory of moving isomorphic sphere.This surface is widely used in water conservancy engineering.Since it both reduce resistance of flow at corner of intersected cylinders and increases strength there.However,when the angle between axis of intersected cylinders become smaller,it is more preferable to use the female surface of the sphere with varied radius.This surface of transition zone with a stable width possesses better avaliable properties.