The programming system discussed here is similar to APT in the definitions it uses. It can automatically generate CNC blocks for the machining of contours and pockets, bounded by linear and circular segments. The system uses simple trigonometry to analyse lines, circles and their intersections. This paper explains a number of algorithms for geometric definitions, elimination of redundant surfaces (thereby optimising the tool path), tool-path generation, etc. A new approach proposed in the present work, based on the construction of a triangle, has simplified the geometry for the case of a circle tangential to two other circles. A number of geometric construction methods and the selection of the milling process (climb versus conventional) for tool-path generation are explained. The system has been modified to machine tapered contour surfaces with a required draft angle.