Reinforced concrete (RC) beams can be strengthened in shear by externally bonded (EB) fibre reinforced polymer (FRP) composites in the forms of side-bonded FRP strips, FRP U-jackets or FRP wraps. The shear failure of almost all RC beams shear-strengthened with FRP wraps and some of the beams strengthened with FRP U-jackets, is due to the rupture of FRP. For an FRP wrapped beam with FRP bonded to the beam surface, debonding of EB FRP from concrete substrate usually precedes the ultimate FRP rupture failure, therefore the failure process of the beam is associated with both FRP debonding and rupture failures. Despite extensive research in the past decade, there is still a lack of understanding of how the failure of FRP wraps in such an FRP-strengthened beam progresses and how it affects the shear behaviour of the beam. This paper presents an analytical study on the progressive failure of FRP wraps in such strengthened beams. In this study, the debonding and the subsequent rupture processes are derived and the FRP contribution to the shear capacity of the beam is quantified. The analytical solution is verified by comparing its predictions with the predictions of a finite element model. An additional merit of the analytical solution is that the development of FRP shear contribution with the opening of the shear crack can be quantitatively determined, providing a useful tool for further investigation on the shear interaction among different components (FRP shear reinforcements, steel shear reinforcements, and concrete) in RC beams shear-strengthened with FRP.