This work was aimed at developing a first approach to produce structural models of the Annulus Fibrosus, i.e. constitutive models of individual lamellae. Parameters of Holzapfel’s model were fitted using literature data on the behaviour of tissue components. Used on sample-specific or simplified geometries, the effect on the whole annulus deformation of the fibre angles, interlamellar behaviour, and incompressibility was analysed to assess their role in the disc mechanics