Abstract Simulation of direct lightning strokes to overhead line towers requires accurate modeling of tower grounding systems. When large-scale statistical simulations are needed (e.g. in backflashover rate assessment), detailed but computationally intensive models are not suitable. This paper presents a genetic algorithm-based procedure to synthesize a generalized pi-circuit model, aimed at simulating the impulse response of complex grounding systems, including non-linear soil ionization, for backflashover studies. The equivalent electrical parameters of the pi-circuit model are determined as functions of soil resistivity for some commonly used grounding systems; the pi-circuit model is then validated by time-domain ATP-EMTP comparison with a complete circuit model, obtaining very good results (worst-case errors do not exceed 3–4%). ATP-EMTP time-domain simulations of direct lightning strokes to overhead lines equipped with the pi-circuit model are also reported, showing an excellent agreement with results yielded by the complete circuit model as well as drastically decreased computation times (up to 3 orders of magnitude).