Extensive research has shown that bonding a thin plate to the tension face of a beam can significantly improve its flexural performance. Such a plated beam often fails by the premature debonding of the thin plate from the original beam in a brittle manner. A sound understanding of the mechanism of such debonding failures is important for the effective use of this strengthening technique. This paper presents a new analytical solution for the interfacial stresses in plated beams subjected to arbitrary mechanical and thermal loads which are symmetrically positioned about the mid-span. While the bonding of fiber reinforced polymer (FRP) plates to reinforced concrete (RC) beams represents the most common application of the plate bonding technique, the present solution is generic in terms of the materials of the beam and the plate. The solution is represented by Fourier series and is based on the minimisation of complementary energy. The new solution takes into consideration the non-uniform stress distribution in the adhesive layer and the stress-free boundary condition at the ends of the plate. In addition, it correctly predicts the drastic difference in the interfacial normal stress between the plate-to-adhesive interface and the adhesive-to-beam interface. The solution is general in nature and may be applied to the analysis of other types of composite structures.