Abstract: In the welding engineering of large-scale pipe structures,the assembly precision and the branch pipe cutting curve of two intersecting pipes haven't been settled for a long time.Based on the engineering practices of pipe structures,a mathematical model used for hemetially sealed intersecting assembly between radially cut branch pipe and uncut main pipe is established.By the solution of the model,a calculating formula of the local dihedral angel of intersecting line and a parametric equation of contacting line are given.At the same time,the mathematical essence is expounded.A branch pipe,practically cut,can be assembled with a main pipe accurately.