In this paper we report on the back-to-back corrugated feed horn design for the High Frequency Instrument on the PLANCK Surveyor. Special single moded Gaussian profiled horns have been developed for the 4 lowest frequency channels (100 GHz, 150 GHz, 217 GHz & 353 GHz). These feed structures produce very pure Gaussian radiation patterns with sidelobe levels reduced well below −30 dB. Similar few moded horn antennas are being proposed for the highest frequency channels (545 GHz and 850 GHz) to give non-diffraction limited performance with high throughput. The modelling of the horns uses a rigorous electromagnetic mode matching technique that is found to give good agreement with measurement.