Abstract: The basic principle and advantage of abandon satellites using an electro-dynamic tether deorbiting system were discussed. The cable model of an electro-dynamic tether system was presented through analyzing the force and moving way of the electro-dynamic tether in Low Earth Orbit (LEO). The virtual work-energy functional was used to obtain the free vibration equations of 2D motion. Numerical solutions to the equations were obtained by using the finite difference method. The numerical solutions show that the 2D model can present the vibration character in deorbiting course, and the vertical response of the cable is far larger than the longitudinal response. Thusly, the vertical response is the main vibration way of an electro-dynamic tether.