In the present work, the effects of various filler types and content on the characteristics and properties of styrene-butadiene rubber (SBR) were studied. This study prepared SBR filled with different fillers: kaolin, metakaolinite, synthetic zeolite Na-A, alumina (Al2O3) nanoparticles, and hybrid filler (synthetic zeolite Na-A/Al2O3). The silane coupling agent 3-aminopropyltriethoxysilane (APTES) was employed to treat the surface with fillers. Scanning electron microscope (SEM) and X-ray diffraction (XRD) were used to determine the surface morphology. The results demonstrated that fillers improved the physicomechanical properties. Tensile strength and elongation at break (%) in composites containing synthetic zeolite Na-A increased by up to 158.6% at 3 phr and 100% at 2 phr, respectively. The results showed that the surface properties displayed by SEM analysis indicated a good distribution of filler particles. Also, the rubber compound’s resistance to organic solvents such as toluene was improved, as evidenced by swelling properties; the swelling ratio decreased by 17.5% while the crosslink density increased by 42.6% at 5 phr Al2O3/synthetic zeolite Na-A. The constants of the various hyperelastic models that explain the behavior of the composite materials under study were determined, and their predictions of the experimentally obtained stress-strain curves were compared. The study’s experimental findings will be helpful for several industrial uses, including an extender in water-based paints, rubber fillers, ceramic materials, paper fillers, and coating pigments.