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 using a mapped infinite element. The source contribution was included in the potential approximation function per finite element. A sufficiently good approximation was achieved with a small number of source images obtained by local mapping of the source within the element on its boundary surfaces. The calculation results were tested on simple examples solvable by the potential method, based on the integral problem formulation. The calculation procedure implemented is simple enough and applicable to a wide range of earth electrodes encountered in practice.