The curing of thermosetting adhesives is a complex polymerization process that involves the transition of a viscous liquid into a viscoelastic solid. This phase transition is frequently accompanied by a volume shrinkage of the material, which may induce mechanical strains and stresses. These, in turn, can lead to a reduced performance or even failure of the adhesive joint. The present contribution introduces a continuum mechanical model that is suited to describe the emergence of stresses and the corresponding initiation of material degradation in adhesive layers, both during the process of curing and, of course, during subsequent loading. The model is implemented into a finite element code and some numerical examples demonstrate the interaction of curing shrinkage, stress evolution, and damage.