The current characterization of asphalt binders is based on linear viscoelasticity wherein the testing is performed under small strains. It ensures that the binder stress response is independent of the strain amplitude and is sinusoidal in nature with frequency same as input frequency. However, the asphalt binders may be subjected to large stains as part of asphalt mixture in the pavement under field conditions and the response may well be nonlinear. The linear viscoelastic measures lose their meaning in the nonlinear range and it is essential to decipher the nonlinear binder response under large stains. In this study, a crumb rubber modified asphalt binder is tested at large strains of 30%, 40% and 50% at an applied frequency of 0.5 Hz and testing temperature of 30°C. A stress decomposition technique based on geometric interpretation of nonlinear response is utilized to obtain the elastic and viscous contributions in the total response. Further, Chebyshev polynomials of the first kind are used to obtain meaningful viscoelastic measures in the nonlinear regime. It is observed that third order elastic and viscous contribution appear in the nonlinear response, and the binder shows strain stiffening and shear thinning behavior under the tested conditions of large strains