One major characteristic of bonded structures is the highly localised nature of deformation near sharp corners, ply-terminations, and ends of joints where load transfer occurs. This paper presents an investigation of the use of a cohesive zone model in predicting the strong effects of stress concentration due to varying adherend thickness on the pull-off strength measured by the Pneumatic Adhesion Tensile Testing Instrument. A comparison is made with the point-strain-at-a-distance criterion, where the plastic deformation of the adhesive is analysed using a modified Drücker-Prager/cap plasticity material model. The fracture properties of the cohesive zone model were determined using double-cantilever and end-notch flexural specimens, and the cohesive strengths were measured using tensile and lap shear tests. Comparisons with experimental results reveal that the cohesive zone model with perfectly plastic (or non-strain-softening) cohesive law provides accurate predictions of joint strengths.