Fibre-reinforced plastic (FRP) materials are increasingly being used for the rehabilitation of concrete structures. Various adhesives are being employed for attaching FRP materials to concrete and for creating force-transmitting joints between structural elements. Although various existing models focus on predicting the behaviour of FRP–concrete composites, a fundamental understanding of the lap-joint behaviour of FRP plates bonded to concrete still needs to be gained. In particular, there is a lack of a simple and reliable method that allows defining the stiffness of the adhesive in the FRP–concrete lap-joint area. In this study, GFRP plates were bonded to concrete blocks incorporating various proportions of silica fume and rice husk ash. A test set-up was developed to induce shear stresses in the GFRP–concrete lap-joint area. Specimens were instrumented with strain gauges at key locations to establish local stress–strain behaviour. Three-dimensional solid finite elements were used to model the GFRP plates and concrete block. The adhesive was modelled as a spring system with stiffness k v and k p simulating the shear and peel rigidity of the adhesive, respectively. Although it still needs future developments, the finite element model thus developed coupled with the simple test procedure provide a simple means for calculating the stiffness of the adhesive between the GFRP and concrete. Knowledge of this stiffness is expected to allow a more realistic modelling of the lap-joint behaviour of GFRP–concrete composites.