The calculation of the surface potential resulting from the earthing system which is exposed to high voltage is very important due to the required degree of human safety, but this estimation is very complicated so the development of a software program to simulate the surface potential at the ground level is required. A new approach for estimating the surface potential of an earthing system arranged by using driven vertical rods is presented. Where the electric potential distribution is obtained by using Laplace's equation which is calculated by using the finite element method. Three models of different numbers of electrodes buried in homogeneous soil are used; model one is represented by one driven rod, model two is represented by three driven rods that are not connected and arranged in a delta shape and finally, model three is represented by three driven rods that are connected and arranged in a delta shape. The strength of the finite element method in this application is its ability to allow a detailed representation of the types of soils used and different models of the simulation models of the rods. The three different models are used for studying the effect of increasing the number of the driven electrodes of the earthing grid on the value of the surface potential resulting from an earthing system that is exposed to high voltages.