The CAD model of a elliptical gear for wire cutting has been developed. The rolling contact of pitch ellipses whose rotation axes coincide with their focus has been analyzed, and the perimeter of the pitch ellipse has been divided into equal-length segments by the number of teeth. A master tooth profile, which is a composite curve of circular arcs that represents involute, has been introduced. The elliptical gear has been designed by imposing the master tooth on the divided points of the pitch ellipse, and a full fillet has been achieved between neighbour teeth. Thus, the whole profile of an elliptical gear is a composite curve of arcs only, and consequently NC codes for wire cutting can be easily generated. Furthermore, a computer simulation program is developed to verify the mesh of the elliptical gear.