This paper proposes a constitutive role for the viscoelastic materials combining iso-butylene and stylene polymers. Part 1 provided highly accurate linear rule under wide range of temperature and frequency. Part 2 proposes and extension of the linear rule wich can consider the strain sensitivities. So-called temperature-frequency equivalency principle is found applicable even under the large shear strain, and it is utilized for efficient analytical modeling of three distinct viscoelastic materials. The nonlinearities under the stable condition as well as the non-stable condition are carefully considered to the model. The model shows excellent accuracy over a wide range temperature, frequency, and shear strain of the sinusoidal loading, as well as random loading such as the building response displacement and the gradually increasing and decreasing displacement.