Concrete, a complex mix of variously sized aggregates, sand, water, additives and cement binder, is one of the more common engineering materials used for the design and construction of structures and bridges. Concrete is characterised by good compressive strength properties but it demands the use of internal reinforcement, generally in the form of round steel bars, to carry tensile stresses. The strength of the resulting element is dependent on the amount and distribution of steel reinforcement included during construction. It is not however possible to include additional internal reinforcement after construction in the event of the applied loading being increased and therefore consideration must be given to strengthening the structure externally, demolishing it, or con®ning it to speci®c usage, for example a maximum weight restriction on a bridge. In circumstances where restricted usage is not practicable structural strengthening is generally more favourable than demolition and replacement. Research in the area of strengthening of existing bridge beams is currently topical in the European Union given recent EU directives, aimed at encouraging free trade and movement of goods and services, which require all bridges to take 40 tonne vehicles.This paper describes the numerical modelling procedures employed, using smeared crack models available in ANSYS V5.4, to capture the load-deformation response and modes of failure, of reinforced concrete beams which have been strengthened, using carbon ®bre reinforced polymer (CFRP) composite material plates. Experimental veri®cations of these simulations have also been performed and are discussed in the present paper.