Describing the hysteresis behavior of magnetorheological (MR) shock absorber significantly facilitates the developers before manufacturing and control processes. However, most of the models developed to describe the phenomenon have been required experimental data of the manufactured absorber. In this study, the hysteresis behavior for a shock absorber has been characterized by developing a three-dimensional coupled numerical model that adapts Viscoelastic Maxwell Model to momentum equations of fluid flow. The viscosity of the MR fluid, which depends on the magnetic flux density, has been calculated with the Herschel-Bulkley model at each node of the fluid domain, coupled with the magnetic field analysis. The hysteresis relationship between force and velocity has been obtained from time-dependent CFD analyses on the deformed grid. It has been observed that the hysteresis behavior of the MR shock absorber has been attained with a good agreement when the data obtained from the developed numerical model are compared with the experimental data. In addition, besides estimating the hysteresis widths in the force-velocity curves, all effects and changes in time in the flow domain have been observed thanks to the model.