Cement-based materials suffer from low tensile strength and poor strain capacity. They are brittle and highly sensitive to cracking, notably to cracking due to length changes whatever the original cause of the length change. This study shows that a partial replacement (by volume) of natural aggregates by rubber aggregates obtained by grinding of used tyres is a suitable solution to improve the strain capacity before the macro-crack formation, conferring to the rubberised concrete a reduced propensity for shrinkage cracking. Moreover, the modulus of elasticity is advantageously reduced and it can be predicted using mix laws such as Hashin-Shrikman low bound considering rubberised concrete as a two-phase composite. Despite its low strength, the elastic quality index (EQI) of rubberised concrete remains in the range of values used for the design of pavements on soil. Besides this potential in terms of pavement application, it is also an interesting way to utilise industrial by-product and consequently a contribution to keep environment clean.