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This paper presents the results of work related to developed mathematical model implementation in order to describe the mechanical properties of magnetorheological elastomers subjected to compressive stress. The used mathematical apparatus is a development of the classical viscoelastic model, which takes into account in its structure the influence of deformation amplitude and magnetic field induction on the progressive nature of recorded stress values. The need to introduce such alterations has been demonstrated as a result of previous research. As part of this paper, the structure of the created numerical model is presented. The simulation results were subsequently included and then compared with the results of previous experiments. This provided the basis for assessing the accuracy of the proposed model.