Using the governing equations developed from earlier work, we analyze a commercially relevant fiber drawing process where draw pins are used for localizing and enhancing the fiber draw. Inclusion of a draw pin introduces the possibility of unloading in the fiber, resulting in the additional complexity of elastic-plastic fiber characteristics in the analysis. In the absence of unloading, the stress in the fiber monotonically increases. so that only the elastic response of the fiber enters into the analysis. In this work, we analyze an isothermal two stage drawing process with a draw pin in the second draw zone. Various possibilities of draw are analyzed, which show that the total draw is in general distributed between the first and the second roller as well as on the pin. The offset location of the pin is shown to have a significant effect on the distribution of the draw. As this offset is increased, the nature of the draw on second roller changes from loading, to neither loading nor unloading at a critical offset, to unloading.