To strengthen concrete or masonry, a modern technique uses adherent strips made of Fiber Reinforced Polymer (FRP). A model problem for this is here considered, represented by an elastic stiffener pulled at one end, in adhesive contact with an elastic half space in generalized plane stress. An analytical solution is developed under the hypothesisà la Baranblatt that cohesive adhesion forces remain active between the two materials when relative slip occurs (provided this is less than a critical value), so that the stress singularity predicted by the theory of elasticity in the case of perfect bonding is removed. We find that the bond length beyond which no further increase of strength could be achieved, referred to as the effective bond length, coincides in practice with the ultimate length of the cohesive zone, i.e., its maximal extension prior that the critical slip limit is attained. The debonding process in a pull-out experiment is analyzed in detail. Results are in better agreement with experimental data than those obtainable with traditional models, which neglect as a rule the deformation of the substrate.