Abstract Research on the application of magnetorheological elastomers (MREs) is one of the key areas of search for structural materials having new, improved properties. These are intelligent composite materials with properties sensitive to the effect of magnetic field. In order to describe the response of a material to the applied forces and the effect of magnetic field we need to derive an adequate mathematical model. This paper presents the results of studies of the behaviour of such composites under compression and the effect of static magnetic field. It also presents the attempts to use rheological models for describing MREs. This modelling method relates to macro-scale and is based on the behaviour of the material under controlled excitation.