The paper presents experimental research and numerical modeling of dynamic properties of magnetorheological elastomers (MREs). Isotropic and anisotropic MREs have been prepared based on silicone matrix filled by micro-sized carbonyl iron particles. Dynamic properties of the isotropic and anisotropic MREs were determined using double-lap shear test under harmonic loading in the displacement control mode. Effects of excitation frequency, strain amplitude, and magnetic field intensity on the dynamic properties of the MREs were examined. Dynamic moduli of the MREs decreased with increasing the strain amplitude of applied harmonic load. The dynamic moduli and damping properties of the MREs increased with increasing the frequency and magnetic flux density. The anisotropic MREs showed higher dynamic moduli and magnetorheological (MR) effect than those of the isotropic ones. The MR effect of the MREs increased with the rise of the magnetic flux density. The dependence of dynamic moduli and loss factor on the frequency and magnetic flux density was numerically studied using four-parameter fractional derivative viscoelastic model. The model was fitted well to experimental data for both isotropic and anisotropic MREs. The fitting of dynamic moduli and loss factor for the isotropic and anisotropic MREs is in good agreement with experimental results. •Dynamic properties of isotropic and anisotropic magnetorheological elastomers (MREs) were measured using double-lap shear test.•Dynamic moduli of the MREs reduce with raising the strain amplitude. Dynamic stiffness and damping of the MREs increase with the rise of the frequency.•The magnetorheological (MR) effect, dynamic stiffness and damping of the MREs enhance with increasing the magnetic flux density.•The anisotropic MREs showed higher dynamic moduli and greater MR effect than those of the isotropic ones.•Dependence of MRE dynamic properties on frequency and magnetic intensity was numerically studied by fractional derivative viscoelastic model.