Drawing is a mechanical operation that changes the material thickness by using the speed difference between the feeding and delivery devices. When the material is in the form of a bundle or bundles made of staple fibers, this attenuation operation is called 'bundle drawing' or g'draftingg'. Drafting is being used widely in manufacturing staple yarns, which is indispensable for the textile industry. However, the bundle processed by this operation has more or less defects in the evenness of linear density. Such irregularities cause many problems not only for the product quality but also for the efficiency of the successive processes. In this research, a mathematical model for the dynamic behavior of the bundle fluid is set up on the basis of general physical laws using physical variables, i.e. linear density and velocity in the dynamic state of the bundle processing. The conservation of mass and the momentum are applied, while the movement of individual material is taken into account. The constitutive model relating the surface force to the deformation of bundle is given, considering a representative bundle movement. Then, a fundamental equation system is simplified in a steady state, which could delineate the characteristics of the process dynamics. On the basis of the simplified model, simulation is performed, and the results are confirmed by experiments. This study shows that the bundle fluid, in drafting operation, can have a jerk at the exit, when the model parameters representing inter-fiber friction and velocity variance of constituent fibers are adjusted to the experimental results. Even at low draft ratios, the bundle can break, if the parameters are not maintained adequately by controlling the process conditions.