This paper presents a new electromagnetic model for the analysis of the harmonic field of mesh earth electrodes placed in a horizontally complex multilayer soil. The model is based on the application of the finite element technique to the integral formulation of the problem. Using the finite element technique, each conductor of the mesh earth electrode is divided into segments and the entire electromagnetic coupling between them is taken into account. The calculation of Sommerfeld integrals is avoided by using an appropriate approximation. The model is very effective and general. It provides a basis for the calculation of currents and potentials along large mesh earth electrodes or an earthing system placed in a multilayer soil. The total number of layers and the total number of metallically separated mesh earth electrodes is completely arbitrary. A single mesh earth electrode can extend through several layers. The effectiveness and generality of the computational procedure is based on the successful application of numerical approximations of two kernel functions in the integral expression for the potential distribution within a single layer created by a point current source. The generalization from a point source to a segment of a grid earth conductor is performed by integrating the potential contribution resulting from a line source composed of point current sources along the axis of the segment. Based on the presented theory, the MATLAB program package Uzemko was developed for the numerical analysis of grid earth conductors laid in horizontally complex multilayer soil. The developed program package provides high-accuracy results and very high-quality graphical output in a short computational time. Using this package, a real problem can be effectively solved on a PC of a common configuration.