Abstract Machining of helical surfaces of constant pitch with tools bounded by surfaces of revolution is accompanied by generation errors due to imperfections of the effective cutting edge, relative positioning errors or kinematics of the machine tool. Therefore, the development of algorithms for the geometrical modelling of helical surfaces could be very useful. In fact, it is possible to model geometrically the effective generated surface on the workpiece when the cutting edge is known at discrete points, for instance, by physical measurement. Based on the principle of minimal distance first proposed in a previous work of the first author, a numerical method is developed that provides a very simple, yet very accurate, means to resolve both the direct and the inverse problem in the machining of helical surfaces with milling cutters and end mills. Thus, the profile of the cutting tool can be determined even for surfaces on the workpiece of arbitrary shape known either analytically or at discrete points. More importantly, it can be established either in the design or the exploitation stage what the accepted errors on the tool are (due to sharpening or wear), such that the tolerances on the surface to be machined are still met.