A numerical formulation of an elasto-damage constitutive model was developed and implemented in a finite element software to investigate the biomechanical response of the periodontal ligament (PDL). The mathematical framework accounts for the description of large strains, anisotropy and inelastic phenomena. The anisotropic mechanical response is caused by the spatial orientation of the sub-structures of the tissue, such as collagen fibres. Inelastic behaviour, induced by high level strains, is modelled by means of damage models. In vitro experimental testing on PDL samples from pigs was performed to obtain tensile stress-strain curves. A finite element analysis is presented in order to define a general numerical approach. A comparison of numerical and experimental data is provided in order to show the reliability and effectiveness of the formulation assumed.