Rapid developments in computer graphics system allows virtual observing the aimed functions of manufacturing system. Because the virtual simulation of chip removal process needs high calculation and graphics, the aimed fundamental processes are handled. In this study, object modelling and interaction algorithm are developed for 3D (3 Dimensional) simulation softwares of CNC lathes. 2D (2 Dimensional) polygon based modelling is used in modelling workpiece and cutting tools. While 2D workpiece model is being subjected to sweep by being rotated, the geometry of 2D cutting tool is sweept linearly, and 3D images are obtained. A 2D polygon clipping technique has been developed for the interaction between workpiece and cutting tool. The functionality has been checked by using the developed system in the virtual verification system.