Hysteric damping is often modelled thanks to linear viscoelastic approaches such as "nearly constant Q" models. These models do not take into account nonlinear effects either on the stiffness or on the damping, which are well known features of soil dynamic behaviour. This paper proposes a mechanical model involving nonlinear viscoelastic behaviour for isotropic materials by which nonlinear elasticity and nonlinear damping are simultaneously taked into account. On one hand the shear modulus is a function of the excitation level ; on the other hand, the description of viscosity is based on a generalized Maxwell body involving non-linearity. This formulation is implemented into a 1D finite element approach for a dry soil. The validation of the model shows its ability to recover flow amplitude ground motion response. For larger excitation levels, the analysis of seismic wave propagation in a nonlinear soil layer on a rigid substratum leads to results which are physically satisfactory (lower amplitudes, larger time delays, higher frequency content).