A progressive cohesive failure model has been proposed to predict the residual strength of adhesively bonded joints using a moisture-dependent critical equivalent plastic strain for the adhesive. Joints bonded with a ductile adhesive (EA9321) were studied for a range of environmental degradations. A single, moisture-dependent failure parameter, the critical strain, was calibrated using an aged, mixed-mode flexure (MMF) test. The mesh dependence of this parameter was also investigated. The parameter was then used without further modification to model failure in aluminum and composite single-lap joints (SLJ) bonded with the same adhesive. The FEA package ABAQUS was used to implement the coupled mechanical-diffusion analyses required. The elastic-plastic response of the adhesive and the substrates, both obtained from the bulk tensile tests, were incorporated. Both two-dimensional and three-dimensional modelling was undertaken and the results compared. The predicted joint residual strengths agreed well with the corresponding experimental data, and the damage propagation pattern in the adhesive was also predicted correctly. This cohesive failure model provides a simple but reliable method to model environmental degradation in ductile adhesive bonded joints, where failure is predominantly within the adhesive layer.