In the human lumbar spine, annulus fibrosus fibres largely contribute to intervertebral disc stability. Detailed annulus models are therefore necessary to obtain reliable predictions of lumbar spine mechanics by finite element modelling. However, different definitions of collagen orientations coexist in the literature for healthy human lumbar annuli. Therefore, four annulus fibre-induced anisotropy models were built from reported anatomical descriptions, and inserted in a L3–L5 lumbar bi-segment finite element model. Annulus models were, respectively, characterized by radial, tangential, radial and tangential, and no fibre orientation gradients. The effect of rotational and axial compressive loadings was simulated and first, predictions were compared to experimental data. Then, intervertebral disc local biomechanics was studied under axial rotation and axial compression. A new parameter, i.e. the fibre contribution quality parameter, was computed in the anterior, lateral, postero-lateral, and posterior annuli of each model, in function of fibre stresses, radial load distributions, and matrix shear strains. Locally, each annulus model behaved differently, affecting intervertebral disc biomechanics and segmental motions. The fibre contribution quality parameter allowed establishing direct links between local annulus fibre organization and local annulus loadings, while other kinematical and biomechanical data did not. It was concluded that functional relations should exist between local annulus fibre orientations and overall segment morphology. The proposed fibre contribution quality parameter could be used to examine such relations and calibrate lumbar spine finite element models by locally adjusting the annulus bundle criss-cross angles. Conclusions of this study are particularly relevant to patient-specific models or artificial disc designs.