This study proposes a procedure to fully characterize and model the Payne Effect. The material used here is filled silicon. First, the master curves of the dynamic moduli are obtained for different dynamic strain amplitude values. Then the continuous spectrum of relaxation time, depending on the dynamic strain amplitude, is identified. This spectrum is discretized into a finite series, in order to be implemented into a constitutive law. A strain energy function is chosen to describe the elastic part of the constitutive model. Concerning the dissipation potential, the viscosity parameters are positive but depend on the dynamic strain amplitude value. It gives a nonlinear viscoelastic constitutive law, modeling the Payne effect.