Since the early 1970s, extensive studies of flow induced vibration in cross flow, especially, fluid-elastic instability, have been reported. Determination of fluid-elastic stability thresholds in tube arrays is very important for design basis. Once large amplitude whirling motions are initiated, the system often does not retrace the response curve as flow velocity is reduced. This is so called hysteresis and is one of the considerations that we must take into account. The objective of this paper is to analyze the hysteresis and determine the critical flow velocity for the flow induced vibrations (FIV). A simple semi-empirical linear model has been developed to determine critical flow velocity. The results of present linear model were compared with those of other theories. These results were better than those of Gorman``s theory in low mass damping parameter region. In addition, nonlinear model has been developed to analyze the hysteresis behavior. As results of the present the nonlinear model for two flexible tubes, the regions of hysteresis behavior were shown. These results were also compared with experimental data which was obtained by Lever and Rzentkowski. The region of hysteresis is an important factor for more conservative design.