Optical design in the terahertz (THz) waveband suffers from a lack of dedicated software tools for modelling the range of electromagnetic and quasi-optical propagation conditions encountered in typical systems. Optical engineers are forced to use packages written for very different wavelength systems and there is often a lack of confidence in the results because of possible inappropriate underlying physical models. In this paper we describe the analytical techniques and dedicated CAD software tools (MODAL1) that we are developing for long-wavelength design and analysis in the THz waveband. Our basic approach to modelling long-wavelength propagation is the application of modal analysis appropriate to the problem under investigation2,3. We have extended this to include the efficient description of common off-axis (tilted) components such as simple curved reflectors4. In earlier research we have investigated the conditions under which approximate methods (ray tracing, paraxial modes) can provide extremely efficient and accurate solutions and situations where a more rigorous approach is required5,6. As a rigorous model of electromagnetic wave propagation, physical optics can be used to characterize complete systems to high accuracy. However, the straightforward approach is computationally intensive and, therefore, not suitable for the initial design or preliminary analysis of large multi-element optical systems. In order to improve the computational efficiency of the usual PO approach we have developed fast physical optics software, initially for the analysis of the ESA PLANCK system7. The MODAL code is modular and multi-platform, and different propagation models can be used within the same framework. Distributed parallel computing enables significant reduction of the time needed to perform the calculations. We present the new software and analyses of the QuaD8 and Herschel (HIFI)9 telescope systems.