At the present time the interaction of Terahertz (THz) radiation with random structures is not well understood. Scattering effects are particularly relevant in this spectral regime, where the wavelength, and the size and separation of scattering centres are often commensurable. This phenomenon can both be used to advantage in imaging and sensing, but conversely can have adverse effects on the interpretation of a "fingerprint" spectrum. A new mathematical method, the Phase Distribution Model, is reported here for the calculation of attenuation and scattering of THz radiation in random materials. This uses a Phase Distribution Function to describe the effect of the non-absorbing scatterers within the media. Experimental measurements undertaken using previously published results, data obtained from specially constructed phantoms and from everyday textiles have been compared with the theory. These experimental results encompass both cylindrical and spherical scattering situations. The model has also been compared with exact calculations using the Pendry code
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