The study describes a numerical approach used to investigate the non-linear behaviour of reinforced concrete beam strengthened with CFRP strip bonded on its soffit. Stiffness method was implemented for the analysis to predict the structural response of the composite beam in elastic as well as inelastic range of loading. The composite beam is divided into a sufficient number of different length segments. The cross section area of the composite beam is also divided into a sufficient number of layers to model different material used in the beam. The inelastic stiffness of the beam is obtained by predicting the actual strain-stress distribution along the depth of the member using incremental-iterative approach. Based on the converged strain distribution along the cross section of different member segments, new flexural and axial stiffness are evaluated for each segment and used to assemble an updated stiffness matrix for the composite member. The algorithm used can predict the inelastic response of the beam in terms of deformation and failure mechanism. The results of the analysis have good agreement with the results observed in experimental testing. © 2006 Civil-Comp Press.