The paper analyzes the problem of modeling lightning strike current for the purpose of determining the radiated electromagnetic field in the environment of a lightning strike to the ground. The aforementioned analysis is otherwise used as part of a broader model for predicting the impact of an indirect lightning strike to the ground in the vicinity of MV and LV overhead lines. The paper describes the existing so-called engineering models of lightning strike current, and their mutual comparison is made. The influence of the input parameters of lightning strike current (e.g. strike speed, etc.) on the behavior of the aforementioned engineering models is also shown.