Forces are generally defined in physics as functions of position (Newton: gravity) or velocity (Laplace: magnetic force on a moving electric charge). Damping forces are little known even today and represent one of the most intriguing subjects of physics. Maxwell elements and fractional derivatives are used to modelize time domain natural hysteretic damping. The resulting models are comparatively complicated and have a limited domain of validity especially when strong non-linearity is involved. The mathematical model we use is based on the introduction of a new state variable and is particularly suitable in the non-linear vibration case. S.I.D. (Strain Integral Damping: see ref. [2]) is a very suitable mean to modelize natural hysteretic damping in the time domain and for nonlinear rubber elements in particular . In the present paper the stress is on modelling of nonlinear elements. The effectiveness of SID is shown by an example concerning a strongly non-linear spring. A ‘’Scilab’’ script is provided to better explain.