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 work took as a starting point a well-known technique which shows that in metals the drilling of a hole at the crack tip induces stress relaxation and slows down its propagation. It shows that a partial replacement of natural aggregates by rubber aggregates obtained by grinding end-of-life tyres is a suitable solution to improve the strain capacity before the crack localization conferring to the rubberized concrete a reduced potential for shrinkage cracking. Unfortunately, experimental results also confirm that the ideal, namely low modulus and high strength are two characteristics mutually exclusive. The modulus of elasticity is advantageously reduced and one can predict this trend using mix laws such as Hashin-Shrikman bounds, considering rubberized concrete as a two-phase composite. It appears that if a low strength is not a bar but a resistance to length changes is a priority, they are some conditions to carry out sustainable applications with a bonus, a contribution for a clean environment by recycling end-of-life tyres.