The present work considers the numerical simulation of the steady-state fracture of adhesively bonded joints in various peel test configurations. The model is based on a multiscale approach involving the simulation of the continuum elastoplastic response of the adherends and the adhesive layer, as well as of the fracture process taking place inside the adhesive layer using a cohesive zone formulation. The model parameters are firstly identified by comparison with experimental results obtained with the wedge-peel test. Secondly, the ability of the model to predict peel test results obtained with different peel test configurations (e.g. wedge-peel or fixed-arm peel test geometries and various adhesive layer or arm thicknesses) is critically assessed by comparison with experimental data. Thirdly, the results of the steady-state simulations are post-processed in order to: (i) evaluate the adhesive fracture energy, (ii) quantify and discuss the different contributions to plastic dissipation within the adhesive layer, and (iii) explain how these mechanisms affect the adhesive fracture energy as a function of the peel test configuration. The values of adhesive fracture energy, Ga, deduced from the numerical simulations proposed in the present paper, from all the various elastic–plastic peel test configurations, lie in the range of about 900±50 J/m2; whilst the values from a previous analytical model and a node-release finite-element analysis model, for a cohesive fracture of the present adhesive, all lie in the range of about 1100±250 J/m2. Thus, there is very good agreement between the different modelling methods. These values are clearly also in good agreement with the corresponding value from the well-established LEFM TDCB method of 1140±170 J/m2.