Problem statement: The objective of this study is to compare the methods for approximating the positions of twist fiber in yarn structures. Computer Aided Design (CAD) is applied using parametric equation, spline curve and NURBS curve. The ideal twist fiber and fiber migration are studied in 3 dimensions. Approach: The fiber positions in yarn structures were measured by trace fiber technique. The twist fiber in rayon yarn with 2.1, 3.0 and 6.0 twist factors was used as examples. The geometrical properties of twist fiber including curvature and torsion were applied in the analysis of all twist fiber examples. Each position was approximated along the length of yarn and then graphical representations of fiber are shown. Results: For ideal twist yarn, using parametric equation gives a smoother or better curve than when using the spline and NURBS curves. However, in the case of fiber migration, continuity of spline and NURBS curves are smoother than that of parametric equation. Conclusion/Recommendations: According to the comparison of the approximation method, parametric equation is most suitable for geometric modeling of ideal twist fiber, whereas the spline and NURBS curves were recommended for approximating the position of migrating fiber.