The present study is devoted to the elaboration and investigation of a composite material based on mechanically grinded recycled tires and a polymer binder. The correlation between the content of the binder, some technological parameters, and material properties of the composite was clarified. The apparent density, the compressive stress at a 10% strain, the compressive elastic modulus in static and cyclic loadings, and the insulating properties (acoustic and thermal) were the parameters of special interest of the present investigation. It is found that a purposeful variation of material composition and some technological parameters leads to multifunctional composite materials with different and predictable mechanical and insulation properties.