Abstract: Rendering photo-realistic animal fur is a long-standing problem in computer graphics. Considerable effort has been made on modeling the geometric complexity of fur, but the reflectance of fur fibers is not well understood. Fur has a distinct diffusive and saturated appearance, that is not captured by either the Marschner hair model or the Kajiya-Kay model. In this paper, we develop a physically-accurate reflectance model for fur fibers. Based on anatomical literature and measurements, we develop a double cylinder model for the reflectance of a single fur fiber, where an outer cylinder represents the biological observation of a cortex covered by multiple cuticle layers, and an inner cylinder represents the scattering interior structure known as the medulla. Our key contribution is to model medulla scattering accurately---in contrast, for human hair, the medulla has minimal width and thus negligible contributions to the reflectance. Medulla scattering introduces additional reflection and transmission paths, as well as diffusive reflectance lobes. We validate our physical model with measurements on real fur fibers, and introduce the first database in computer graphics of reflectance profiles for nine fur samples. We show that our model achieves significantly better fits to the measured data than the Marschner hair reflectance model. For efficient rendering, we develop a method to precompute 2D medulla scattering profiles and analytically approximate our reflectance model with factored lobes. The accuracy of the approach is validated by comparing our rendering model to full 3D light transport simulations. Our model provides an enriched set of controls, where the parameters we fit can be directly used to render realistic fur, or serve as a starting point from which artists can manually tune parameters for desired appearances.