The Electrogeometric Method (EGM) is commonly used to analyze and design the external lightning protection of power transmission lines. However, it has been found that the EGM is not able to predict the shielding failure rate observed in EHV and UHV transmission lines. In this article, an analysis of the lightning attachment to EHV and UHV transmission lines is presented, using the Self-consistent Leader Inception and Propagation Model (SLIM). The study is focused on the effect of operating voltage and type of terrain on the estimated lightning attraction distances for overhead transmission lines. It is found that the phase conductors have slightly larger lightning attraction areas during their positive voltage semi cycle and much more over mountainous terrain.