The diploma thesis deals with the design of concrete structures reinforced by FRP according to ACI, fib, CSA and EC2 regulations, which are stressed by a shear force. The diferences between steel rebar and FRP reinforcement were described, in particular its mechanical degradation over time and a different stress-strain diagram. Furthermore, shear capacity calculations were performed according to the regulations and compared with the real tests. Then the parametric analysis of shear strength was performed. In the practical part, the design of concrete floor slab structure supported by the pillars and walls was performed. The upper reinforcement of this slab was designed with FRP and the lower with steel rebar. Double-headed studs were used as a punching shear reinforcement.