The behaviour of adhesively bonded joints is investigated using a continuum mechanical description for the adhesive. The gradient of the adhesion variable, which describes the volumetric proportion of cavities within the adhesive, is introduced in the free energy, so that the model accounts for the intrinsic cohesion of the adhesive. The adherends are linear elastic materials and the adhesive is first given an elastic behaviour. Using a thermodynamical framework, an adhesion potential function is established, the subdifferential of which is determined in a rigorous way, so that three-dimensional coupled elastic-adhesion evolution equations are derived. Then we consider a generalization to the coupling of adhesion with elastoplasticity. A two-dimensional model of adhesive bonding is derived using a perturbation method. Finally, a finite element discretization of the coupled evolution problem is presented and a resolution scheme based on Newton's method is developed, while the integration of the constitutive law is performed using a three-step operator splitting method.