Lots of research carried out on externally bonded carbon fiber reinforced plastics (CFRP) showed that such strengthening of RC bent elements is not fully effective because of the stress concentrations caused by stiff epoxy adhesive layers with Young’s modulus ranging in 4-15 GPa. A solution for this problem is the use of flexible polyurethane (PU) adhesives instead of stiff epoxy ones. This system was developed at the Cracow University of Technology and was investigated using various polyurethane adhesives of orders lower stiffness than epoxies, with Young’s modulus ranging in 2-8 MPa. Such flexible adhesive layers transfer high loads and high deformations simultaneously and it is possible to obtain a cohesive failure in the PU layers, protecting the concrete substrate against failure. Inexpertly, load-deflection characteristics of these carbon fiber reinforced polyurethane (CFRPU) systems are similar or even more efficient than the CFRP ones. Computational models for RC elements strengthened with externally bonded CFRP systems follow the Bernoulli’s hypothesis of plane cross-sections. In the CFRPU system, bent layers should be modeled with the use of the Bernoulli–Euler beam theory and, with regard to the adhesive layers of small rigidity, the adhesive is approximated with the simple shear state. This analytical approach related to the results of experimental tests carried out on beams strengthened with CFRP and CFRPU is presented and compared with experimental results. Obtained analytical and experimental results manifest good compatibility with the potential to provide designers with simple engineering calculations.