The aim of this paper is to mathematically describe and analyze the viscoplastic properties of a magnetorehological (MR) fluid. The scope of the discussed research has been limited to the T-MR SiMR 132 DG damper prototype. Laboratory tests have been performed on a specially developed experimental stand with a kinematic excitation rule. On the basis of the experimental data, conventional yield points and maximum shear stresses for the analyzed MR fluid, including variable shear rate, current intensity flowing through a solenoid, liquid temperature and gap height have been analyzed. Basing on the acquired results, the parameters of Bodner-Partom constitutive equations have been estimated. The identified viscoplastic model has been used to carry out simulation tests that enabled verification of the numerical results and real experimental data.