This paper proposes an efficient way to calculate the transient electromagnetic field coupling to overhead multiconductor transmission lines (MTLs) in the time domain based on the Gauss-Seidel iterative algorithm analytically. This method is performed in the time domain directly. Thus, the case that transient electromagnetic field coupling to MTLs terminated by nonlinear load can be analyzed conveniently. In this method, the cross-coupling between the conductors is represented by the equivalent distributed voltage and current sources along every lines. Then, the analytical expressions of the voltage and current response along MTLs are derived iteratively in time domain based on the Gauss-Seidel iterative algorithm. The proposed method is validated by several numerical examples, which demonstrate that the proposed approach could handle the case that MTLs terminated by the linear load and the case that MTLs terminated by the nonlinear load with the acceptable computational accuracy. The proposed method exhibits a higher convergence rate than the previous Jacobi iterative method, especially for the case where the MTLs have a high ratio of length to wavelength and the case in which the MTLs have a high coupling factor. Additionally, due to the analytical methodology that the proposed method adopts, the computational accuracy is not affected by the simulation time step. Therefore, the proposed approach is very efficient for modeling of the transient electromagnetic field coupling to long overhead multiconductor transmission lines.INDEX TERMS Overhead transmission line, analytical method, transient response, Gauss-Seidel iteration.