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Geometry of a screw fabricated by a turning process determined by the shape of the tool, feed rate of the tool and rotation speed of the spindle. Therefore, computing the exact geometry of the screw is very important to perform a simulation on machining or an evaluation of the workpice quality. In this paper, a new mathematical geometry model of the 3 dimensional screw is fabricated by turning process introduced for the exact geometry computation. Becasue model has a parametric formulation, it is easy to process for a CAD geometry or apply for a machining simulation. Also, it can be applied to process planning because it gives precise machined geometry on whole the 3 dimensional surface of the screw. This paper introduces a new parametric model of a geometry for screw fabricated by turning process. As an application, a simulation software for the 3 dimensional screw surface is developed and evaluated for several manufacturing parameters.