We present Gaussian fitting parameters of simulated beams of the High Frequency Instrument (HFI) of the ESA PLANCK mission. This space probe is designed for measuring the anisotropy of temperature and polarization of the Cosmic Microwave Background (CMB). The six HFI spectral bands cover the frequency range 0.1 - 1 THz with 52 bolometers. Their beams are computed by multi-mode physical optics propagation of the source field from the apertures of the horns simulated by the scattering matrix approach. Computed power patterns are fitted by the elliptical Gaussian beams minimizing the peak difference between the two power distributions within the beam. This approximation is generally considered as acceptable from the scientific viewpoint, although we show that induced errors are far from negligible.