The difficulty of degradation and storage of rejected tyres has led to increasing environmental problems, beyond the proliferation of insects which may transmit diseases becoming a harmful residue to the public health. This work investigates the physical and mechanical properties of polymeric composites based on tyre rubber wastes in order to achieve a sustainable material which is in accordance with international construction standards. A full factorial design of experiments of type 2231 was used to analyze the results. The experimental factors investigated were: particle size (30/50 US-Tyler and 100/200 US-Tyler), volume fraction (10, 25 and 50%) of rubber particles and the addition of maleic anhydride (1.5%) as a compatibilizing agent. The investigated responses in this experiment were: bulk density, apparent porosity and compressive strength. The rubber particles of 100/200 US-Tyler provided the increase of density and strength of the composites. The increase of rubber fraction reduced the density and strength, however, the level of 25% of rubber exhibited acceptable properties for engineering applications. The maleic anhydride affected the properties of the composites mainly when the rubber particle size is at 30/50 US-Tyler and rubber fractions at 10 and 25%.