The design of concrete mixtures incorporating tire rubber waste particles often leads to hardened concretes of inferior performances. Yet, the use of rubber waste in concrete represents a sustainable solution to reduce natural aggregate depletion. It also allows to better manage the growing amounts of tires in the environment. In order to evaluate the effect of incorporating rubber particles on the mechanical properties of fiber-reinforced concretes (FRC), two rubber particles sizes were selected: [2–5 mm] and [5–8 mm], to replace 5% by volume of either sand or gravel or both. Silica fume was also added to the mixtures at 10% by mass of cement, as it is deemed to play an active role in filling the cement pore structure and in densifying the paste-aggregate Fetcinterface, the aim being to mitigate the decrease of resistance that the rubber-based concretes might witness. The results obtained from the splitting tensile and compressive tests, show that the rubber concretes exhibit slight resistance drops, but overall, the values are within the same order of magnitude as the control specimens. The results also seem to point toward the possibility of using rubber tire particles, up to the tested substitution rate, in the process of designing eco-friendlier fiber-reinforced concretes.