As part of the correct operation of any electrical system, it is necessary to guarantee the safety of the persons and the equipment or elements that constitute the system. Therefore, an electrical traction system must be furnished with a grounding system that takes into account their particularities and differences with regard to other electrical systems. This paper proposes a generalized multi-train model to simulate the behavior of the rail voltage and the stray currents in the grounding system, based on equivalent circuit models, processing the instantaneous power obtained from a multi-train DC transport systems electrical demand simulator.