The aims of this study were to assess the damage and failure strengths of lamellar fibrous tissues, such as the anterior annulus fibrosus (AF), and to develop a mathematical model of damage propagation of the lamellae and inter-lamellar connections. This level of modelling is needed to accurately predict the effect of damage and failure induced by trauma or clinical interventions. 26 ovine anterior AF cuboid specimens from 11 lumbar intervertebral discs were tested in radial tension and mechanical parameters defining damage and failure were extracted from the in-vitro data. Equivalent 1D analytical models were developed to represent the specimen strength and the damage propagation, accounting for the specimen dimensions and number of lamellae. Model parameters were calibrated on the in-vitro data. Similar to stiffness values reported for other orientations, the outer annulus was found stronger than the inner annulus in the radial direction, with failure at higher stress values. The inner annulus failed more progressively, showing macroscopic failure at a higher strain value. The 1D analytical model of damage showed that lamellar damage is predominant in the failure mechanism of the AF. The analytical model of the connections between lamellae allowed us to represent separately damage processes in the lamellae and the inter-lamellar connections, which cannot be experimentally tested individually.