Consideration of moment redistribution (MR) in the design of continuous reinforced concrete (RC) beams results in an efficient and economical design. Adding fibre-reinforced polymer (FRP) materials to reinforced structures to enhance flexural capacity leads to a reduction in ductility, such that design standards severely limit use of the MR in their design. This has forced engineers to use elastic analyses for strengthening design, which can lead to FRP wastage. To overcome this, complicated or empirical solutions have been applied to solve the problem of MR in strengthened concrete members, with limited success. This paper presents a novel theoretical strategy for quantifying and tracking MR in such members by employing basic structural mechanics without any need for estimating rotation capacity or ductility. Fully non-linear flexural behaviour of continuous strengthened members can be predicted and any geometry, loading arrangement and strengthening technique or configuration can be considered. The numerical model is validated against existing experimental data from the literature. Good agreement is shown between the experimental and numerical data, with the significance of this work being that, potentially, for the first time MR could credibly and confidently be incorporated into design guides for FRP strengthening of RC structures.