This analysis of the milling process shows that the path of a milling-cutter tooth is an arc of a trochoid, the parametric equation for which can be derived from known variables of the cut. As a result, the milling process is susceptible to mathematical treatment. Practically, the advantage of such analytical methods is that such elements as the radius of curvature of the tooth path, the clearance and rake angles of the length of the tooth path, the radial thickness of the chip, and their effects upon the quality of milled surface may be evaluated. The paper demonstrates the advantages of the up-milling process in achieving machined surfaces of high quality. This form of analysis will also be found useful in comparing different milling methods.