Groundings are necessary parts included in lightning and shock protection. In the case of a surge current, high current phenomena are observed inside the grounding. They are a result of the electrical discharges around the electrode when the critical field is exceeded in soil. An available mathematical model of grounding was used to conduct computer simulations and to evaluate the influence of current peak value on horizontal grounding parameters in two cases. In the first simulations, electrodes placed in two different soils were considered. The second case was a test of the influence of current peak value on grounding electrodes of various lengths. Simulation results show that as soil resistivity increases in value, the surge impedance to static resistance ratio decreases. In the case of grounding electrodes lengths, it was confirmed that there is a need to use an operating parameter named effective grounding electrode length, because when it is exceeded, the characteristics of grounding are not significantly improved during conductance of lightning surges. The mathematical model used in the paper was verified in a comparison with laboratory tests conducted by K.S. Stiefanow and with mathematical model described by L. Grcev.