Abstract: To achieve the cutting of opening and welding mating surface in two intersecting pipes by five-axis linkage CNC machine, this paper introduced a mathematical model about irregular saddle shape hole based on analytic geometry and principle of numerical integration after analyzing interpenetrating model of eccentric pipes. A model of welding mating surface with blunt edge was established based on the riding type and insertion type of lap welding. This paper analyzed the processing methods and the accuracy of CNC machine based on the model. Related data were generated by AutoCAD VBA programming. By comparing with the physical models produced by rapid prototyping (KP) technology, the result verifies the reliability and generality of mathematical models for the opening and welding mating surface and the accurate control method. It also illustrates the RP technology had many advantages in simulating and lapping of circular pipes.