Elastomers, due to their excellent damping and energy absorption characteristics and low cost are used extensively in automobile industry to isolate the structures from vibration and shock loads. In this study, it was aimed to analyze the damping performance of an elastomer buffer embedded in the suspension of an automobile. To reach to this aim, vibration simulation of an automobile suspension model was conducted by using a nonlinear explicit finite element code, Abaqus. In order to simulate the damping behavior of elastomer buffer, the hyperelastic and linear viscoelastic material models were used together. The numerical model was validated with results of exact solution method in terms of transmissibility ratio and phase shift in a wide range of input excitation frequencies. Good agreement was observed between the exact solution and finite element results, which indicate that finite element model is sufficiently accurate. To examine the damping performance of the buffer, the displacement time history curves were extracted for suspension with and without buffer under the sinusoidal base excitation. The vibrating motions of suspension for both conditions were compared. The comparison results proved that the elastomer buffer was effective in improvement of damping performance of suspension. It reduced the amplitude of vibration and oscillation time of sprung mass remarkable in excitation frequencies around and over the natural frequency of the system.