Â© 2014 SPIE. In this paper we describe the optical modelling of astronomical telescopes that exploit bolometric detectors fed by multimoded horn antennas. In cases where the horn shape is profiled rather than being a simple cone, we determine the beam at the horn aperture using an electromagnetic mode-matching technique. Bolometers, usually placed in an integrating cavity, can excite many hybrid modes in a corrugated horn; we usually assume they excite all modes equally. If the waveguide section feeding the horn is oversized these modes can propagate independently, thereby increasing the throughput of the system. We use an SVD analysis on the matrix that describes the scattering between waveguide (TE/TM) modes to recover the independent orthogonal fields (hybrid modes) and then propagate these to the sky independently where they are added in quadrature. Beam patterns at many frequencies across the band are then added with a weighting appropriate to the source spectrum. Here we describe simulations carried out on the highest-frequency (857-GHz) channel of the Planck HFI instrument. We concentrate in particular on the use of multimode feedhorns and consider the effects of possible manufacturing tolerances on the beam on the sky. We also investigate the feasibility of modelling far-out sidelobes across a wide band for electrically large structures and bolometers fed by multi-mode feedhorns. Our optical simulations are carried out using the industry-standard GRASP software package.