The use of Fiber Reinforced Polymer (FRP) is becoming a widely accepted solution for repairing and strengthening of deteriorated reinforced concrete members, to restore their load carrying capacities. One of the major concerns in the use of FRP is its cost. This therefore calls for the use of efficient and cost effective design approach. Design efficiency in terms of cost can be achieved through optimisation. In the present paper, Generalized Reduced Gradient (GRG) optimisation technique was employed to optimize the strengthening cost of a simply supported reinforced concrete beam strengthened with Fibre Reinforced Polymer (FRP). Optimum design charts for the considered problem were presented. The results showed that considerable savings in thickness can be achieved using FRP of high modulus of elasticity. For example at very high capacity reduction say 70% (kc = 0.3), the required FRP thicknesses for FRP with elastic moduli of 25GPa, 50GPa, 75GPa, 100GPa, 125GPa and 150GPa are respectively equal to 2.5mm, 1.75mm, 0.75mm, 0.6mm, 0.5mm and 0.4mm. http://dx.doi.org/10.4314/njt.v36i1.7