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This study presents a generalised mathematical model through which the propagation characteristics of high-voltage (HV) transient pulses along a multi-wire electric fence line, which has discontinuities as a result of loads, faults and branches, can be accurately predicted. The fence line, which has an earth return path, is modelled in the frequency domain to facilitate an analytical solution for the propagation of HV pulses along the line. The discontinuities are modelled by dividing the fence into sections at discontinuities and representing each section between two discontinuities as a two-port network. The boundary conditions for each section are derived in relations to the other sections and initial conditions, to realise a solution in the frequency domain. The frequency domain solution is then transformed into time domain by means of a numerical Laplace inversion algorithm to determine the propagation characteristics of the line at a given location and time. Simulations of power systems computer-aided design and experimental results confirm that the proposed fence model is accurate, and can thus be considered as an invaluable tool at the design phase of electric fence energisers.