This study develops a coupled multiphysics finite element method for the dynamic analysis of a bare flexible electrodynamic tether. Contrary to the existing methods, the new method discretizes and solves the orbital motion limited equation and the dynamic equation of an elastic flexible tether simultaneously. First, the new method is verified via comparison with the existing methods in a straight tether situation. Second, the number of tether elements, tether bending deformation, and two design parameters at the cathodic end affecting the electrical current are investigated. It is determined that the tether bending deformation and the two parameters i.e., the impedance Z T and Φ PW have a significant impact on the electron collection efficiency of an electrodynamic tether system. The results indicate that the proposed method should be applied in the refined mission analysis.