The primary concern of this thesis is the development of theoretical and computational techniques for the modelling of cavity coupled bolometric detectors for future millimetre wave and terahertz astronomical receivers. Hypersensitive bolometer based receivers will be required to answer current open questions in astronomy concerning star and planetary formation, solar system physics as well as galaxy evolution and interaction. As part of the work for this thesis, fast and efficient Python code, GAMMA (Generalised Absorber Mode Matching Analysis), was developed and applied to existing and proposed future systems. One of the main goals of GAMMA was to analyse the performance of the proposed multimode pixel for the SAFARI instrument on the next generation SPICA terahertz space telescope. The pixels contain a free space gap between the horn and the cavity. The array of detectors will lie on a chip with an array of horns feeding them from the frontside and an array of backshort cavities behind them. The beam patterns for a SAFARI-like pixel were computed, using a direct calculation of the power absorbed by the bolometer in free space. This shows how the formalism can be used to directly calculate the power absorbed by a detector in a realistic terahertz receiver system. The impact of the various potential manufacturing tolerance levels for the feed horn on the predictions of the beam on the sky were also analysed for a millimetre-wave system. The specific example considered was the new 4 mm receiver on the Onsala Space Observatory 20 m millimetre-wave telescope. Mode matching, Gaussian Beam Mode Analysis and Physical Optics were used to determine the behaviour of the optical relay system. GAMMA was also applied to the multimode 857 and 545 GHz ESA Planck HFI channels. Agreement between previous predictions and both laboratory and in-flight measurements reported in literature was improved on.