The primary goal of this work is to test and model the magnetorheological (MR) properties of the isotropic magnetorheological elastomers (MREs) under the coupled static–dynamic compressive loads. Isotropic MREs with different contents of magnetic particles were fabricated based on the silicone elastomer. In order to apply the controllable magnetic field to the MREs and directly measure the viscoelastic force of the deformed MREs during the dynamic tests, an electromagnet with a magnetic flux density of up to 0.9 T was developed and integrated into an electric dynamic test system. The stress–strain hysteresis loops of the produced MREs were experimentally characterized under the dynamic compressive loads coupled with different static pre-strains. Effects of particle content, strain amplitude, static pre-strain and load frequency on the MR properties of the MREs were examined in terms of the characteristics of the hysteresis loops, as well as the MR effects in the storage modulus, loss modulus and pre-stress. The results revealed that irrespective of the applied magnetic field, the deformation behavior of the produced MREs was in an approximate linear viscoelastic state when the strain amplitude was less than 7.5%. Both the absolute and relative MR effects increase with the increasing particle content, and decrease with the increasing strain amplitude. Only the absolute MR effect increases with the increasing pre-strain. While varying the load frequency has almost no effect on the MR effect of the MREs. Furthermore, two empirical models were proposed respectively for predicting the storage modulus and loss modulus of the MREs as functions of the magnetic flux density, particle content, strain amplitude, pre-strain and load frequency. The graphical comparison and quantitative evaluation show that the proposed models can give effective predictions of the storage and loss moduli of the produced MREs under the applied load conditions in this work.