The aim of this project is the modelling of single-mode step-index fibre and slab waveguides in the terahertz range. This will be done by a combination of several analytical and numerical methods and we will derive the relevant theory. We will look into mode profiles, mode coupling by evanescent waves and transmission and reflection in several geometries. For a 200 µm diameter air-silica step-index fibre, we find that single-modes exist for frequencies below 0.607 THz. The coupling length between two identical silica slab waveguides of thickness 200 µm ranges from a few hundred micrometres to several meters due to substantial evanescent waves. The reflection of slab waveguide in several geometries remains low usually below 1 %. Whereas the transmission of the guided mode in a layer of a waveguide suspended in the air to a layer with foam instead of air is highly dependent on the refractive index of foam. The same holds when the guided mode is incident from the waveguide-foam layer to the waveguide-air layer.