The article considers the nonmetallic composite woven material used to reinforce exploited concrete structures. It has been demonstrated that the main factor ensuring the reliability of the construction is the composite woven material bonding to concrete of the reinforced concrete structure. The authors present an innovative technique for the experimental evaluation of the composite woven material bonding to concrete. The schemes of destruction of the flexural members externally reinforced with a composite woven material have been established. It has been proved that the external reinforcement by composite materials must provide the inclusion of the reinforcement elements in operation with the reinforced structure, while the reinforced concrete structure remains a complex technical system. The authors have carried out experimental studies of the structures reinforced with composite materials of various types. Reinforced concrete beams with working fittings of A500 class and with reinforcement of A600 class reinforced with canvases made of fiberglass and coal as well as with carbonamines were tested. At the ends of some of them, there were U-shaped anchors made of composite material. The reinforcement of the beams was done by sticking carbon fiber on the stretched fabric, the number of layers of carbon fiber varied from 1 to 4. As test samples, beams with a length of 1290 mm with a cross section of 120x190 were used. The beams reinforced with a single layer of carbon fiber were destroyed when the latter detached, the steel samples underwent destruction over the concrete of the compressed zone. The reinforcement of the beams increased the bearing capacity up to 130%. The article outlines the main directions for the development of researches on the structures with the composite woven reinforcement.