This paper presents multi-physics modeling of a MR absorber considering the magnetic hysteresis to capture the nonlinear relationship between the applied current and the generated force under impact loading. The magnetic field, temperature field and fluid dynamics are represented by the Maxwell equations, Conjugate heat transfer equations and Navier-Stokes equations. These fields are coupled through the apparent viscosity and the magnetic force, both of which in turn depend on the magnetic flux density and the temperature. Based on a parametric study, an inverse JilesAtherton hysteresis model is used and implemented to the magnetic field simulation. The temperature rise of MR fluid in the annular gap caused by core loss (i.e. eddy current loss and hysteresis loss) and fluid motion are computed to investigate the performance of current-force behavior. A group of impulsive tests were performed for the manufactured MR absorber with step exciting currents. The numerical and experimental results showed good agreement, which validates the effectiveness of the proposed multi-physics FEA model.