QUaD is a ground-based high-resolution (up to l ≈ 2500) instrument designed to map the polarisation of the Cosmic Microwave Background and to measure its E-mode and B-mode polarisation power spectra. QUaD comprises a bolometric array receiver (100 and 150 GHz) and re-imaging optics on a 2.6-m Cassegrain telescope 2. It will operate for two years and begin observations in 2005. CMB polarisation measurements will require not only a significant increase in sensitivity over earlier experiments but also a better understanding and control of systematic effects particularly those that contribute to the polarised signal. To this end we have undertaken a comprehensive quasi-optical analysis of the QUaD telescope. In particular we have modelled the e...