Abstract: Flow-structure interaction problems are ubiquitous in nature. In this paper, the Immersed Boundary Method (IBM) is introduced to simulate the process of the flapping flexible body in the flow field from static status to steady movement, and we found that there are three modes in the wake of flapping flexible body, i.e. the small strength Karman vortex street will change into the irregular chaotic state from the beginning, and it will be showed great strength Karman vortex street in the wake when the flapping movement is steady. With the bending strength decreases, the vorticity increased and the time of modal translation is moved up. When the flapping state is stability, the bending strength do not show obvious effects on the wake in flow field, but the drag coefficients are not decreased, just only the suitable bending strength will reduce the drag of flexible body in flow field. It is a certain reference value to discuss this question for the biological differences in response time and the improvement of engineering efficiency.