For a long time and until now, rubber is the most used material for the manufacture of tires for motor vehicles. Unfortunately, once the tire meets its life cycle, the remaining rubber cannot be recycled, so the tires are discarded in collection centers and often in clandestine dumps. This represents a serious environmental problem because, in one case, these waste tires become breeding grounds for insects and wildlife that is harmful to humans. In the second case, the tires are burned, releasing highly damaging gases into the atmosphere. On the other hand, concrete is worldwide the construction material par excellence. It is basically composed of cement, gravel and sand. Mixing these three components in different proportions, their mechanical strength in compression can be increased. However, due to its fragile nature, concrete, once a crack is formed, it rapidly advances by fragmenting the material and producing its rapid collapse. In the present work, in order contribute to the care of the environment as well as to modify the fracture mode of the concrete, rubber particles obtained from waste tires were used as sand substitute in hydraulic concrete. In addition, rubber modified samples concrete were lately exposed to 70 kGy of gamma radiation in order to study the effects of this radiation on the mechanical deformation of concrete. The results showed a decrease in the mechanical properties of the concrete with rubber particles with respect to the traditional concrete itself. However, such decreases were offset by the fact that samples with rubber addition do not collapses as fast as the free rubber samples. The acquired data pave the way for research with great benefits, such as the use of recycled tires in concrete for its fracture mode modification in a beneficial way, as well as a possible decrease in the cost of concrete.