Connective fibrous tissues, such as tendons and ligaments, in humans and animals exhibit hyperelastic behaviour. The constitution of the material of these tissues is anisotropic due to the presence of the collagen fibres, where one family of fibres is the typical case. Traumatic events and/or aging may sometimes lead to the damage of the tissue. The study of motion of affected joints or limbs is usually not permitted in vivo. This is where finite element method (FEM) becomes useful as a premise for general analysis, surgical planning or designing of implants and medical treatment. One of the most often used FEM commercial programs is the field of the biomechanics is Abaqus. The present study discusses the potential of user subroutine UANISOHYPER_INV in this code to analyse response of transversely isotropic tissue with damage in quasi-static range. This subroutine requires providing the material energy function and its derivatives only. The stress tensor and constitutive matrix are computed by the software automatically. To the best of the Authors’ knowledge this procedure provides the easiest way to simulate the anisotropic hyperelastic material behaviour in Abaqus. In this study its usage is extended onto the damage response simulation. The verification of the approach and its validation against experimental data indicates its efficiency.