This paper presents a method for determining the elastic shear and peel stresses in an adhesive joint between a strengthening plate and a functionally graded beam (FGB). The beam is assumed to be isotropic with a constant Poisson's ratio and exponentially-varying elastic modulus through the beam thickness. Stress distributions, depending on an inhomogeneity constant, were calculated and presented in the form of graphs. It is shown that the inhomogeneities play an important role in the distribution of interfacial stresses. This research is helpful in understanding the mechanical behaviour of the interface and design of hybrid structures. The results presented in the paper can serve as a benchmark for future analyses of functionally graded beams strengthened by fibre reinforced polymer plates. (C) Koninklijke Brill NV, Leiden, 2010