A linearization method based on the work of Nguyen [Analyse systématique du concept de comportement linéaire équivalent en ingénierie sismique, PhD., université Paris-Est; EDF; ESTP, Cachan (2017)] is extended in this paper. The method is based on the fitting of the relative acceleration transfer function of a linear SDOF oscillator on non-linear relative acceleration transfer functions to obtain the equivalent dynamic parameters in terms of frequency and viscous damping ratio. This paper proposes formulas for the fitting and introduces an additional parameter in the non-linear transfer function numerical calculation. Elastic perfectly plastic, linear kinematic hardening and non-linear kinematic hardening materials behaviors are considered. The cases of wide and narrow band input motions are explored. The linearization method results are compared to formulas from the literature and evaluated according to goodness of fit criteria. The method gives good results regarding relative speed and acceleration values and less accurate results regarding the maximum displacement prediction. This method should be considered in the case of the determination of transferred motions and fatigue analysis.