Magnetorheological elastomers (MREs) are a kind of smart materials, which change the mechanical properties (viscoelastic characteristics) under the magnetic field action. In the paper the determination of damping properties (reactive force) of specimens made out of magnetorheological elastomers is presented. The specimens made out of MREs have been fabricated as a composite with matrix made out of silicone rubber with certain contents of magnetisable particles (carbonyl iron powder). The cylindrical specimens have been tested in compression loading, controlled by an electro-mechanic system. The MRE characteristics of the specimens have been determined in the presence of a magnetic field produced with an electromagnet (coil device). The reactive force occurring in the MRE specimen has been determined on the basis of the measured data during loading. The variation curves of the reactive force versus magnetic field induction are drawn. As a conclusion, the rigidity of the MRE specimen is increasing since the magnitude of the magnetic field induction is increasing.