The size dependence of the flexural strength of concrete beams is discussed. It is shown that existing approaches fail to predict the strength of real-sized structures. The scaling of the modulus of rupture σu can be consistently modelled by means of a multifractal scaling law, the influence of microstructural disorder being predominant for the shallowest beams. At larger scales, homogenization comes into play, leading to the definition of an asymptotic constant strength ft. This transition occurs more rapidly in the case of high-strength concrete, where a more brittle behaviour is observed, accompanied by the rapid vanishing of size effects. Validation of the law is pursued by means of best-fitting of relevant experimental data, which allows for determination of the asymptotic value of σu, valid for real-sized members.