In this paper, the problem of debonding in flexural members strengthened with FRP layers bonded on their tensed and compressed faces is investigated using the fracture mechanics theory. This problem is particularly relevant to double sided FRP applications for the strengthening of masonry or reinforced concrete walls to resist cyclic or dynamic loading. The paper adopts an analytical methodology and compares between two fracture mechanics based approaches for the assessment of the initiation, evolution, and stability of the debonding process. The first approach uses the nonlinear fracture concept of the cohesive interface. The second approach adopts the classical fracture mechanics concept of the energy release rate. In both models, the effect of geometrical nonlinearity and buckling of the compressed layer and its role as the driving force for the debonding process are considered. The two approaches are compared and emphasis is placed on the stability of the debonding process and the post-debonding behavior. These aspects are illustrated through a numerical study that focuses on a masonry specimen strengthened with double-sided FRP systems and subjected to flexure. Conclusions on the behavior of the unique structural system, its stability, and its handling using the fracture mechanics approaches close the paper.