Abstract: This paper presents mathematical principles and methods for the fiber path and machine path design of composite elbows, based on which a CAD system is developed. The main features of this system are: (1) Designing stable fiber paths fulfilling all the technical requirements for filament winding; (2) Generating laminate data for Finite Element Analysis; (3) Generating control data for four-axis winding machine; (4) Real-time simulating the fiber paths and machine paths. The fiber paths designed by this system are stable, non-bridging and uniformly cover the mandrel.