This study is concerned with modeling and analyzing a nonlinear elastomer impact phenomenon when a mass experiences a collision with the contact pad mounted on the underlying linear dynamic structure. The contact pad which consists of the viscoelastic elastomer is modeled here by a nonlinear contact stiffness and nonlinear contact damper. The underlying dynamic structure is measured by a Fourier spectral analyzer and its analytical form is utilized in modeling and analyzing the whole dynamic impact problem. The impact force profiles are predicted and analyzed in terms of pulse duration, time-to-peak force, and peak force. Finally, the damping mechanism and its hysteresis phenomena are also discussed.