The scientific work is devoted to the improvement of the calculation methodology of reinforced concrete elements, using verification of the FRP delamination prevention, during structures strengthening with a system of composite materials (SCM) from various fibers types. During strengthening of reinforced concrete elements with composite material systems, the role of adhesion between concrete and FRP is of great importance due to the fragility of the failure mechanism due to delamination (loss of adhesion). The adhesion strength is generally much higher than the tensile strength of the concrete, so delamination always starts in concrete itself with the separation of FRP layer of different thickness. According to the load-bearing capacity requirements, such a failure mechanism should not precede the failure of the strengthened element during bending or shear. To solve the problem of possible strengthening delamination of composite materials systems, it is necessary to consider different failure modes of FRP. Due to imperfection of domestic building codes, a detailed analysis of the solution to the problem of FRP delamination was carried out in accordance with the recommendations of a number of foreign regulatory documents (ACI, CNR, FIB). The main failure modes, with subsequent initiation of delamination of FRP material from concrete base, are systematized, namely: FRP delamination due to surface irregularities, separation of FRP due to shear cracks, longitudinal shear stresses in the yield zone, excessive deformations in FRP material (FRP rupture), longitudinal shear stresses near the FRP edges, failure in anchoring (fixing) zone of FRP material. Six criterions are proposed that need to be verified during design of structures strengthening systems with FRP materials. During formulation of specified criterions, the main theoretical aspects necessary for application in structural calculations of the studied connection are given. The results of research can be used in future during the design of structures joints strengthening with systems of composite materials based on carbon fibers, glass, aramid. Keywords: system of composite materials, external reinforcement, FRP strengthening, reinforced concrete, failure mode, calculation, delamination.