Abstract Hybrid magnetorheological elastomers (HMREs) were manufactured from sponges filled with magnetorheological suspensions (MRSs) made of silicone oil (SO) and carbonyl iron in 10%, 30% and 60% volume fractions (Φ). The HMREs were obtained from polymerisation of a solution containing silicone rubber (SR), catalyst and MRSs. Flat capacitors (FCs) were manufactured using HMREs as dielectrics, and Cu-reinforced planar structures with graphene nanoparticles (nGr) embeded as electrodes, and the electric resistance (R) and capacity (C) of these FCs were measured as a function of the gradient (δ) of the applied magnetic field. Based on the as-determined C(δ)Φ and R = R(δ)Φ dependences, it is shown that both the dielectric and elastic behavior of the HMREs are influenced by the applied magnetic field and to an extent that depends on the volume fraction Φ. The obtained results are presented and discussed in terms of the dipolar approximation, by assuming the HMRE as a linear elastic body.