In this paper a full-scale commercially available magnetorheological (MR) brake installed in a semi-active suspension (SAS) system is modeled and simulated. Two well-known phenomenological hysteresis models are explored: Bouc–Wen and Dahl ones. In particular, influence of their parameters on the response is evaluated and assessed. The next step is to introduce the artificial neural networks and discuss their application in the field of systems identification. Subsequently, two feedforward neural networks are created and trained to estimate parameters characterizing each of the MR damper models described. The semi-active suspension (SAS) system equipped with a MR brake is described and the detailed procedure for acquisition of the reference data used in the models validation stage is elaborated. The models outputs obtained by simulating them with the values of coefficients as identified by the networks are compared to each other as well as to the reference experimental data. Thanks to that, the comparative analysis between the suggested vibration suppression models and the full-scale MR brake is done and it is concluded which of the discussed models has a better performance. The usability of neural networks in the field of parameters estimation of the mathematical models of the real world phenomena is described as well. The novelty of the presented methodology is the application of artificial intelligence methods to estimate model parameters of a MR brake utilized in a SAS system. The results of this approach have a strong potential to be successfully implemented in the area of model-based control of semi-active vibration suppression systems.