This thesis is concerned with the high-frequency quasi-optical modelling of telescope systems, with special attention paid to the Planck satellite, but further work is also performed on the Stratosphere-Troposphere Exchange And climate Monitor Radiome- ter (STEAMR) and the Far Infrared Instrument (FIRI). The primary work surrounds the modelling of far sidelobe (FSL) patterns of the Planck telescope, with a view to replicating features seen in some of the difference maps made by the 857-GHz channel of Planck's High Frequency Instrument (HFI). This is done using a variety of techniques in a number of software packages. The General Reector Antenna Software Package (GRASP9) is used for accurate characterisation of the FSLs using two analysis methods: Physical Optics (PO), and Geometrical Optics (GO) with the Geometrical Theory of Diffraction (GTD). This is then compared against two simplified paraxial lens models of the telescope, namely the Projected-Aperture (PA) technique and Gaussian Beam Mode Analysis (GBMA). PA is performed by Fresnel integration of fields from source to sky, while GBM requires decomposition of a field into a set of Gauss-Laguerre modes which are propagated from source to sky using a ray matrix formalism. The motivation for analysing the Planck FSL structure is to test the assumption that features in the difference map are a result of manufacturing imperfections in the detector horns. To test this hypothesis a number of altered horn geometries are modelled using the NUI Maynooth Experimental Physics departments in-house waveguide mode-matching soft- ware called SCATTER, and these are then used in the analysis of the telescope system. Further use of SCATTER is illustrated in work on ultra-Gaussian horns for STEAMR, and here it is tested against commercial waveguide modelling software Microwave Wizard (uWW). Further modelling is performed for the Cardiff test-bed of the Planck telescope simulator, which was used for qualification of the Planck HFI ight horns pre-launch. Here we test the hypothesis that manufacturing imperfections could be missed if the effects on beam pattern were imperceptible to measurement. This is done using GRASP9, as is the modelling of FIRI, a multi-beam spectral/spatial interferometer which will hopefully break current constraints on angular resolution obtainable at infra-red wavelengths. In general, this thesis aims to provide insight into the modelling of quasi-optical telescope systems, with particular emphasis on multi-moded systems, providing useful information for future data analysis by the Planck project team.