A mesh-independent continuum damage model has been proposed to predict the residual strength of adhesively-bonded joints by introducing a displacement-based damage parameter into the constitutive equation of the damaged materials. This approach was originally developed for EA9321-bonded single-lap joints and this paper extends it to butt joints bonded with a different ductile adhesive (E32). This involves not only a different adhesive and joint configuration but the high hydrostatic stress requires a more realistic yielding model. A dry and a partially saturated steel joint were used to calibrate the moisture dependent damage parameters of the adhesive E32, and then these parameters were used without further modification to predict the failure of the other environmentally degraded steel butt joints and the aluminum butt joints. The FEA package ABAQUS was used to implement the coupled mechanical-diffusion analyses required. A von Mises yield model was used initially. Then, a linear Drucker-Prager plasticity model was used, as this could incorporate the hydrostatic stress dependency found in the adhesive. The predicted joint residual strengths agreed well with the corresponding experimental data, which exhibited a significant reduction in strength on exposure to moisture but still retained a cohesive failure mode in the adhesive. The mesh independence of the model was also demonstrated.