This paper evaluates and compares two material constitutive models for the finite element analysis of structural adhesively bonded joints in large industrial bonded structures. The first model is a classical bi-linear traction–separation model whereas the second model is a more advanced pressure-dependent elasto-plastic-damage model. On one hand, both models predict different global force–displacement responses when simulating small lab experiments where the adhesive layer is confined between thick metal substrates, such as a Thick Adherend Shear Test. On the other hand, these differences become negligible when simulating the deformation and fracture behaviour of adhesive bonds in industrial benchmarks. These differences are extensively discussed and interpreted carefully and a special attention is paid to the compromise between computational accuracy, computational efficiency and modelling simplicity, which are key requirement to the transfer of such material constitutive models to the industry.