The paper presents the theoretical basis of the so-called of the Liew-Mar model for the analysis of overvoltage conditions on an overhead line (power line) that occur as a result of a close (indirect) lightning strike. It is an analytical model that, among other things, takes into account the influence of the steepness of the lightning current front on the realized water overvoltages. On the basis of the aforementioned theoretical basis, a corresponding computer program was developed in the work, which then analyzed the influence of close lightning strikes on the occurrence of overvoltage conditions in typical MV transmission lines while varying characteristic values such as the height of the conductor above the ground, the distance of the lightning strike from the overhead line, the height of clouds above the ground , the speed of the lightning strike, the steepness of the lightning current front. In addition, the results obtained by the mentioned model were compared with the results of the calculations carried out using the so-called Chowdhuri-Gross model.