An analysis of different methods for calculating mesh earthing systems is carried out in order to determine the best method that can achieve the set goal. In addition to the required calculation time, other characteristics of the methods are also compared, such as the number of linear equations, the symmetry of the system matrix, the fineness of the division, the accuracy of the approximation and the degree of accuracy of the calculation of potentials and touch voltages. All presented methods are performed as special cases of the general projection method, i.e. the moment method of solving integral equations.