Double-enveloping reducer is widely used in the industry due to its high transmission torque and high accuracy. The screw theory and the rigid-body transformation method are introduced and applied in this thesis to the determination of the worm surface. The equation of the worm surface is derived by the two methods based on different geometries of cutting tools (conical cutter and fly cutter). According to the Standards of American Gear Manufacturers Association (AGMA6030 C-87), the size and the shape of the cutters can be determined to conform the worm offset surface. Moreover, a measuring system is set up with a CMM (coordinate measuring machine) to measure and record the center point of the touch probe when it contacts with the surface of the double-enveloping worm. Finally, comparisons of measured results with different theoretical worm offset surfaces obtained from two types of cutting tools are made in this study. Geometric errors of the measured worm offset surface shows that the worm used in this thesis was machined by cutters with a conical form.