In this paper, we study a class of active materials named magneto-rheological elastomers (MREs) with a main focus on their coupled magneto-mechanical response. Based on the theoretical framework proposed by Triantafyllidis [1], we develop the coupled magneto-mechanical constitutive laws in order to identify the corresponding model’s material parameters. The experimental data, obtained with a novel experimental setup allowing tensile tests up to large strains and under high magnetic fields, provide the constitutive parameters needed as input for subsequent numerical simulations.