The anulus fibrosus (AF) is a lamellar, fibrocartilaginous component of the intervertebral disc, which exhibits highly anisotropic behaviors in tension. These behaviors arise from the material’s unique collagen structure. We have investigated the use of a linear, fiber-induced anisotropic model for the AF using a quadratic strain energy density formulation with an explicit representation of the collagen fiber populations. We have proposed a representative set of intrinsic material properties using independent datasets of the AF from the literature and appropriate thermodynamic constraints. The model was validated by comparing predictions with previous experimental data for AF behavior and its dependence on fiber angle. The model predicts that compressible effects may exist for the AF, and suggests that physical effects of the equivalent “matrix,” “fiber,” “fiber–matrix,” and “fiber–fiber,” interactions may be important contributors to the mechanical behavior of the AF.