Tubular Daylighting Devices (TDDs) are systems that collect and channel daylight from building roofs into deep interior spaces. To meet high standards of building energy efficiency and glare-free indoor environments, TDD technologies have been rapidly and continuously evolving over the past two decades. However, this pace has been counteracted by a lack of reliable computer design tools. This paper presents the development of analytical models to compute the optical characteristics (transmittance, reflectance and layer absorptances) of various types of complex TDDs. New metrics for the optical and lighting performance are developed. The optical models are based on the ray-tracing technique, and account for the spectral (monochromatic) or broadband optical properties of TDD glazing panes. Experimental validation of these models is presented in an accompanying paper (Laouadi et al., 2013c).