In this master’s thesis, the types of grounding in the power system are listed and explained. An overview of grounding systems and the division of grounding conductors according to shape and purpose, which serve to protect against atmospheric disturbances, such as lightning strikes that cause very high amounts of lightning current, is given. The paper deals with methods for modeling grounding systems, presenting the theoretical background. It is an antenna theory derived from the full-wave model, when it comes to the thin-wire approximation and the transmission line model based on telegraph equations in the time domain. An analytical model of the transient response of the horizontal grounding electrode, based on the model of antenna theory, is presented, in which the expressions for the scattered voltage at the beginning of the horizontal grounding electrode in the frequency domain are given. The expression for the scattered voltage at the beginning of the horizontal grounding electrode in the time domain obtained by applying the inverse Laplace transform is also presented. The theoretical background of the used approximations, numerical integration and discrete Fourier transform, is given. Approximations used in the analytical model of the transient response of the horizontal ground electrode were analyzed. An analysis of the influence of the approximations used on the accuracy of the calculations in the time and frequency domain is given, changing their parameters. The approximations analyzed are the inverse fast Fourier transform (IFFT) and numerical integration. A comparison of the results of the scattered voltage at the beginning of the horizontal grounding electrode, obtained in the time domain, and in the frequency domain with the application of the IFFT is presented. By changing the parameters of numerical integration and IFFT, the analysis was performed for two forms of lightning strike pulse, and for different values of medium conductivity, with changing the length of the horizontal ground electrode.