A third-order theory of shear deformation is used for description of a stress-strain state of concrete shells reinforced with external composite laminates. Reinforced concrete structures play a key role in civil engineering. Corrosion of steel re-bars used for reinforcement of concrete structures is currently urgent, this problem complicated due to porosity of concrete. To get an adequate solution of the problem of strengthening and retrofitting of degraded structures, external composites bonded to the faces of concrete structures are widely used. Deformation of such kind of structures is highly nonlinear. For the development of nonlinear geometric and material models, we resort to the numerical methods, in particular, to a finite-element method. In the analysis of composite laminates, high-order shear deformations are more and more required. The proposed theory is an alternative to the first-order one developed by Ferreira et al. earlier. The theory has been approbated on a shell element which structure represents a layered discretization of laminate materials. For modeling of the deformation of concrete in compression, perfectly plastic behavior and strain-hardening plasticity of the material have been considered. We have discussed a dual criterion of yielding and fracture of the material in terms of stresses and strains which is supplemented with a broken-line representation of tension deformation curve, the horizontal portion of this line corresponding to the beginning of yielding. The behavior of unidirectional composites is linear-elastic (brittle). Finite-element analysis of a stress-strain state of a concrete bar reinforced with composite strips has been performed for three-point bending. The observable reinforcement effects are described, results of the application of the third-order theory and comparative analysis of the reinforcement of a concrete structure with composite strips and the steel are given.