When flying in formation, the downstream individual maintains a proper state of motion in the wake produced by the upstream individual, which has an important impact on reducing drag and saving energy. In this paper, the influence of flexibility on the motion of a semi free filament in a vortex street is investigated by using the immersed boundary method. The numerical simulation results show that when the filament flexibility changes, the change of filament motion state is related to the flow field conditions. When｜VГy｜/｜Vp｜is less than 0.175, the motion state of the filament remains unchanged by changing the flexibility of the filament, and the filament moves around the vortex cores in the vortex street. When 0.175<｜VГy｜/｜Vp｜< 0.3, the filaments swing adaptively on the side of the vortex street. By reducing the flexibility of the filament, the motion state of the filament will change from moving on the side of the vortex street to moving around the cores. When 0.3≦｜VГy｜/｜Vp｜, the motion state of the filament remains unchanged by changing the flexibility of the filament, and the filament swings adaptively on the side of the vortex street. Compared with the motion around the cores, when the filament moves on one side of the vortex street, the drag decreases obviously. The numerical simulation results in this paper provide valuable reference for the flexible design of aircraft in formation flight.