In addition to the conventional modes of failure observed in RC beams, some premature modes of failure can be observed in beams strengthened by means of externally bonded plates or sheets such as concrete cover delamination or peeling-off of the CFRP sheet. This kind of failure is caused by shear transfer mechanisms and local regions of tension at the interface between the concrete and CFRP. A series of tests was carried out in order to study the concrete cover delamination failure, wherein the variables were length of beam span, bonded area, number of plies, and U-jacketing schemes. Two failure mechanisms within the concrete cover delamination were observed. One was caused by cover delamination at the cutoff point of the sheets, Failure Mode I, which was originated by a high concentration of normal (out-of-plane) and shear stresses. A second one, called Failure Mode II, caused by cover delamination starting from an intermediate flexural crack between the outermost crack and the maximum bending area. The latter mode of failure was originated by splitting of concrete at the steel reinforcement level, and, mainly, by normal and shear stresses at the level of the steel reinforcement. The use of U-jackets is shown to lessen the effect of cover delamination. The mechanisms of the observed modes of failure are described. For Failure Mode I, an analytical approach to estimate the shear and normal stresses at the curtailment of FRP sheets is presented. The mechanism of Failure Mode II is complex. Schemes intending to predict the failure are presented. They can include the analysis of an element between two flexural cracks and the assumption of certain normal stress distribution similar to that employed for Mode I. This may serve as framework for future investigations.