The strengthening of reinforced concrete structures using externally bonded steel or advanced fibre reinforced plastic (FRP) composites is becoming increasingly common. A key factor affecting the behaviour and reliability of such strengthened structures is the bond strength between the steel or FRP plate and the concrete substrate. Several different experimental set-ups have previously been used to determine bond strength. This paper presents a careful finite element analysis of the stress distributions in these test set-ups. Results show that stress distributions can be significantly different for different set-ups, for similar materials and geometry.