The paper presents a detailed analysis of appropriate electrical impedance models for steel railway rails suitable for power supply circuit transient calculations. It extends existing models to fully describe the skin effect, so that power circuit transient behaviour can now be taken into account with little error in prediction of response. Practical measurements of rail impedance are compared with calculated values of circuit impedance and demonstrate an accuracy of within 9% for resistance and 18% for inductance. An associated paper shows how this model can be used to predict remote short-circuit-fault substation current profiles.