The calculation of the electric field of a mesh earth electrode in karst soil was performed using the finite element technique with a combination of differential and integral problem formulation. The combined formulation enabled us to divide the calculation area into a small number of large finite elements, and the openness of the calculation area was solved by using mapped infinite elements. The contribution of the source is included in the function of the approximation of the potential per finite element. A sufficiently good approximation was achieved with a small number of images obtained by local mapping of the source within the elements on its boundary surfaces. The calculation results were tested on simple examples solvable only by the integral formulation using the mean potential method. The calculation procedure implemented is simple enough and applicable to a wide range of earth electrodes that occur in practice.