The inter-lamellar connectivity of the annulus fibrosus in the intervertebral disc has been shown to affect the prediction of the overall disc behaviour in computational models. Using a combined experimental and computational approach, the inter-lamellar mechanical behaviour of the disc annulus was investigated under conditions of radial loading. Twenty-seven specimens of anterior annulus fibrosus were dissected from 12 discs taken from four frozen ovine thoracolumbar spines. Specimens were grouped depending on their radial provenance within the annulus fibrosus. Standard tensile tests were performed. In addition, micro-tensile tests under microscopy were used to observe the displacement of the lamellae and inter-lamellar connections. Finite elements models matching the experimental protocols were developed with specimen-specific geometries and boundary conditions assuming a known lamellar behaviour. An optimisation process was used to derive the interface stiffness values for each group. The assumption of a linear cohesive interface was used to model the behaviour of the inter-lamellar connectivity. The interface stiffness values derived from the optimisation process were consistently higher than the corresponding lamellar values. The interface stiffness values of the outer annulus were from 43% to 75% higher than those of the inner annulus. Tangential stiffness values for the interface were from 6% to 39% higher than normal stiffness values within each group and similar to values reported by other investigators. These results reflect the intricate fibrous nature of the inter-lamellar connectivity and provide values for the representation of the inter-lamellar behaviour at a continuum level.