Abstract: According to spatial analytic geometry,the mathematical model of intersecting of pipe and cone was established.The geometry shape of intersecting curve welding groove at the end of pipe was described in parameters equation.The mathematical model could be used in flame numerical control(NC) pipe cutting machine,and the machine's three axis could move together.The movement of NC cutting of welding groove for intersecting of pipe and cone was also analyzed.The torch movement was divided into three axis motion,rotation around the pipe,travel along the pipe,and bevel in axis section.The parameters for NC cutting such as intersecting curve,dihedral angle,torch bevel angle were expressed in parameters equation.And transition cutting was studied in order to solve small angle problem,and parameters in transition cutting were also given.The results of practice showed that the parameters of welding groove met the requests of American Petroluem Institute criterion.