The effects of strain rate and temperature on the tensile behavior of silicone rubber were investigated. The quasi-static uniaxial tensile experiments were conducted using an electromechanical testing system, and the high-rate uniaxial tensile tests were performed employing a modified split Hopkinson tension bar technique for low-strength and low-impedance materials. The tensile responses were obtained at strain rates of 0.001–1400 s−1 and temperatures ranging from −50 to 50 °C. The experiments reveal that the tensile stress–strain behavior of silicone rubber is nonlinear and highly dependent on strain rate and temperature. The values of stiffness and nominal stress at a given elongation increase with increased strain rate and decrease with increasing temperature. It is appropriate to postulate that the tensile response at high strain rates arises from the combination of hyperelasticity and viscoelasticity. According to the incompressibility assumption, a phenomenologically inspired visco-hyperelastic model was proposed to describe the constitutive behavior of silicone rubber over wide ranges of strain rates and temperatures.