D.C electrified traction systems are a potential source of stray currents. The important problem, technically, is to evaluate the harmful effects (electrolytic corrosion) that an electrified railway has on nearby earth–return circuits (e.g. pipelines). This phenomenon is stochastic and may aggravate electrochemical corrosion in different places depending on the position of the vehicle, the load current, soil parameters, etc. The electric circuit approach, based on the complete field method of solution of the transmission–line problem (the earth–return circuit theory), to model stray currents interference on extended structures is presented. The electrode kinetics (polarization phenomenon) is taken into account in the model developed. Random algorithm allows to explore the phenomenon of polarization for different cases, which allows for generalization of the conclusions regarding the risk of corrosion in the studied systems.