An analytical model of light propagation in rectangular light pipes, termed the flux confinement diagram (FCD), is developed. Based on the edge ray concept of nonimaging optics, the FCD is a construction that describes the angular distribution of flux propagating in a light pipe depending on a light pipe's index of refraction and its geometry. With the FCD model, the angular "mode" of a ray can be defined at any plane in the system. The FCD model is developed here and used to describe flux input coupling, transport, and output coupling in light-pipe illumination systems. The practical example of a flux loss prediction due to a geometrical change (a bend) is examined using the FCD and compared to a ray-tracing analysis. We discuss how this model of flux propagation is a useful tool to aid in "first-order" design and layout of light-pipe illumination systems.