Abstract. The study of cosmic microwave background (CMB) anisotropies represents one of the most powerful cosmological tools. After the great success of the two NASA satellite missions COBE and WMAP, P is the third generation of mmwave instruments designed for space observations of CMB anisotropies within the new Cosmic Vision 2020 ESA Science Programme. P will map the whole sky with unprecedented sensitivity, angular resolution and frequency coverage, using two instruments that share the focal region of a 1.5 m off-axis dual reflector telescope: the Low Frequency Instrument (LFI) and the High Frequency Instrument (HFI). In the optimisation of the optical interfaces of the LFI two concurrent demands have to be satisfied: the very good angular resolution (which affects the ability to reconstruct the angular power spectrum of the CMB anisotropies at high multipoles) and a very low level of straylight contamination (which may be one of the most serious sources of systematic effects). We present the results of the optical simulations aimed at establishing the trade-off between angular resolution and straylight rejection, carried out for the 100 GHz channel of the P LFI. Antenna patterns of different models of dual profiled corrugated conical feed horns have been simulated using advanced simulation techniques, considering the whole spacecraft geometry in order to obtain reliable sidelobe predictions. We show the optical computation accuracy necessary to provide strong straylight evaluation in reasonable computational time and demonstrate the inadequacy of a Gaussian feed model in realistic far beam predictions.