Investigation on the fire resistance of fibre-reinforced polymer (FRP) reinforced concrete (RC) is essential for increased application of FRP bars in the construction industry. Experimental tests for determining the fire resistance of RC elements tend to be expensive and time-consuming. Although numerical models provide an effective alternative to these tests, their use in case of FRP RC structures is hindered because of the insufficient constitutive laws for FRP bars at elevated temperatures. This paper presents the details of a numerical modelling work that was carried out for simply supported carbon FRP (CFRP) and hybrid (steel-FRP) bar RC beams at elevated temperatures. Constitutive laws for determining temperature-dependent strength and stiffness properties of CFRP bars are proposed. Numerical models based on finite element modelling were employed for the rational analysis of beams using the proposed constitutive laws. The behaviour of concrete was simulated by means of a smeared crack model based on the tangent stiffness solution algorithm. The employed numerical models were validated against previous experimental results. The theoretical rebar stresses were calculated in both the FRP and steel bars, and the differences are discussed. Copyright © 2012 John Wiley & Sons, Ltd.