In this paper, we introduce a modified FDTD model in order to investigate the behavior of the induced voltage of a non-uniform transmission line (TL) excited by lumped voltage sources or external electromagnetic wave. The parameters to be taken into account for this specific coupling phenomenon are explicitly analyzed and the affection on the behavior of the induced voltage is discussed in detail. To confirm the validity of this model, results obtained by this model, for two typical transmission line configurations, are compared to results obtained by other models, already published in the literature. Finally, several numerical calculations of the line responses are provided for non-uniform TL's that can be present in practical configurations. These results indicate that a configuration slightly different from the uniform one can cause large discrepancies on the termination voltages of the TL.