The European Space Agency (ESA) Planck satellite has been studying microwave and submillimetre sky with unprecedented sensitivity and high angular resolution since August 2009. The High-Frequency Instrument (HFI) on Planck has observed simultaneously in six bands in the range from 100 GHz to 857 GHz. The inclusion of non-CMB bands allowed for removal of foreground sources from the data. This paper is concerned with the modelling of the specialized multi-mode feedhorns used in the highest-frequency channel centred on 857 GHz. Multi-mode systems have the advantage of increasing the throughput, and thus sensitivity, of the detection assembly when diffraction-limited resolution is not required. The horns were configured in a back-to-back setup which transmits the signal through filters to a detector horn. The modelling of the broadband beam patterns on the sky requires careful analysis of the complex propagation properties of the horns. This presentation describes the approach to modelling the highest frequency, 857 GHz, channel and discusses how the electromagnetic modelling of the horns predicts the beam patterns on the sky and the spill over at the telescope mirrors.