Bundle consists of fibers that have a length distribution, which influences the flow dynamics in a roller drafting process. Since the dynamic behavior of bundle in the flow system can lead to the thickness variation of the output, the fiber length distribution was taken into the dynamic model describing the bundle flow, and the dynamic characteristics and the output bundle thickness were investigated by simulation, while the process factors such as the draft gauge and the draft ratio were considered. Introducing velocity variance models for different fiber length distributions and a simplified sinusoidal velocity variance into the bundle flow dynamics, the output bundle thicknesses were compared each other. The state variables in a steady state showed that the bundle with a uniform fiber length can get a stronger jerk than the bundle with a fiber length distribution, when crossing over the front roller nip line. The bundle flow dynamics could be characterized by oscillatory behavior with a decaying magnitude or an increasing magnitude with an upper limit, which is dependent on the process variables. It was confirmed theoretically that as the draft gauge increases, the output bundle thickness becomes more uniform, while the draft ratio has the opposite effect on the out-put. The critical draft gauge that defines the bordering zone between unstable and stable behavior of the output bundle thickness was about 1. 25 times of the maximum fiber length. The critical draft ratio revealed different results for bundles with a uniform fiber length and a fiber length distribution: for the uniform fiber length the critical draft ratio has a value below than 25, for a fiber length distribution it lies in the zone greater than 25, which demonstrates that the fiber length distributed bundle is roller drafted better that the uniform fiber length bundle. The simplified velocity variance model could be effectively applied to describe the flow dynamics that consists of bundles with a fiber length distribution or even with a uniform fiber length.