This paper deals with Magneto-Rheological (MR) damper modelling and identification. The effect of the frequency and current is analysed through a database of four experimental datasets with different displacement and current. The benchmarking of modified models of a literature model approach is done. It is clarified the linearity of the current with the maximum damping force and its effect on the hysteresis; and if the displacement and current have persistent magnitude variation, the model parameters can be frequency independent. A resultant model based on these findings has realistic behaviour with a simple structure, two non common model features for this device.