Bundle flow occurs in the processes where material with long shape in comparison with its cross-section is used and the process products often undergo thickness fluctuation due to the flow dynamics. This study deals with investigating the stability of a bundle flow by means of theoretical simulation. Introducing perturbation in the flow state demonstrated that the eigenvalues of the linearized flow dynamic system, determining the stability of the flow state, were dependent on the model parameters and the draft ratios. The stability diagram revealed that the stable area of the parameters became narrower as the draft ratio increased, which indicates that the state of the bundle flow is sensitive to the input bundle properties. As the fiber cohesion of the bundle or the draft ratio increased, the flow was apt to change to an unstable state. Especially there existed a specific value of the draft ratio that represented a characteristic measure, addressing the criterion of the bundle flow stability. The bundle flow dynamics was insistently stable under the condition of the draft ratio less than the characteristic value, no matter what values of the parameters were given.