A constitutive elasto-plastic model with moisture diffusion is developed for determining the cohesive strength of adhesively bonded single lap joints with identical adherend materials and thicknesses under tensile-shear loading. Static maximum shear stress failure theory is used for determining the cohesive strength. A Fickian diffusion model is utilized in order to formulate a time- and location-dependent shear modulus for the adhesive. The study shows that increased plastic strain due to moisture diffusion would increase the cohesive failure load of adhesively bonded single lap joints.