Magnetoreological elastomers are an important group of non-classical engineering materials. The aim of the work is to investigate the magnetic field influence on a number of mechanical properties of composites from this group. On the basis of earlier analyzes, the limited usefulness of the classical model of the viscoelastic body to describe the stress-strain relationship of magnetorheological elastomers has been demonstrated. There is therefore a need to propose changes to this rheological model. This article contains theoretical considerations related to the mathematical derivation of dependencies concerning the influence of the strain amplitude on the progressive character of the mechanical hysteresis loops of the discussed materials. It also presents a detailed analysis of the derived equations, along with a discussion, supplemented by a description of simplifying assumptions.