This paper provides an efficient way to simulate the transient electromagnetic field coupling to overhead multi conductor transmission lines in time domain based on an analytical iterative technique. The method is entirely in time domain and therefore can handle straightforwardly nonlinear loads. In this method, the interaction between the line conductors are represented by distributed sources, and the time domain analytical expressions of the transient response along transmission lines are derived step by step by adopting the waveform relaxation and Gauss-Seidel iteration techniques. The efficiency of the proposed method for both linear and nonlinear loads is demonstrated through validation examples. The numerical performance of the method, in terms of accuracy and CPU time, are found to be superior to that of conventional FDTD method. Furthermore, the proposed method allows to obtain similar accuracy as in FDTD with considerably larger time steps. The method is therefore very efficient for evaluating the transient response of long overhead multi-conductor transmission lines illuminated by external electromagnetic fields.