Abstract A numerical method for estimating the curvature, deflection and moment capacity of FRP reinforced concrete beams is developed. Force equilibrium and strain compatibility equations for a beam section divided into a number of segments are numerically solved due to the non-linear behaviour of concrete. The deflection is then obtained from the flexural rigidity at mid-span section using the deflection formula for various load cases. A proposed modification to the mid-span flexural rigidity is also introduced to account for the experimentally observed wide cracks over the intermediate support of continuous FRP reinforced concrete beams. Comparisons with experimental results show that the proposed numerical technique can accurately predict moment capacity, curvature and deflection of FRP reinforced concrete beams. The ACI-440.1R-06 equations reasonably predicted the moment capacity of FRP reinforced concrete beams but progressively underestimated the deflection of continuous ones. On the other hand, the proposed modified formula including a correction factor for the beam flexural rigidity reasonably predicted deflections of continuous FRP reinforced concrete beams. It was also shown that a large increase in FRP reinforcement slightly increases the moment capacity of FRP over-reinforced concrete beams but greatly reduces the defection after first cracking.