High impedance faults (HIFs) and the associated electric arc is a topic of public safety and concern because fault currents are generally too small to be detected in a reliable way by conventional over-current relays. This study proposes an analytical model for analysing HIFs in power distribution systems. The proposed analytical model considers the complex interaction between a time-varying fault impedance, the power distribution line and an equivalent source impedance at the substation bus. Hence, this approach requires the joint solution of a partial differential equation and a single non-linear equation. The proposed methodology calculates the transient conductance, voltage and current at the substation bus, considering several contact surfaces and short circuit levels. The analytical model was validated by means of comparisons with measurements in a real distribution system, results published by other authors and computer simulations in electromagnetic transient programs. The obtained results show good agreement between the analytical model, measurements and computer simulations. A sensitivity analysis of the interaction of all the parameters associated to HIFs is also presented.