Repairing and strengthening structural members by bonding composite materials have received a considerable attention in recent years. The major problem when using bonded FRP or steel plates to strengthen existing structures is the high interfacial stresses that may be built up near the plate ends which lead to premature failure of the structure. As a result, many researchers have developed several analytical methods to predict the interface performance of bonded repairs under various types of loading. In this paper, a numerical solution using finite - difference method (FDM) is used to calculate the interfacial stress distribution in beams strengthened with FRP plate having a tapered ends under thermal loading. Different thinning profiles are investigated since the later can significantly reduce the stress concentration. In the present theoretical analysis, the adherend shear deformations are taken into account by assuming a parabolic shear stress through the thickness of both beam and bonded plate. The shear correction factor for I-section beams is also included in the solution. Numerical results from the present analysis are presented to demonstrate the advantages of use the tapers in design of strengthened beams.