Magnetorheological elastomers (MREs) are ferromagnetic particle impregnated elastomers whose me- chanical properties are altered by the application of external magnetic fields. Due to their magne- toelastic coupling response, MREs are finding an increasing number of engineering applications. The objective of this work is (a) the experimental study of transversely isotropic MREs (i.e., particles form chains along a certain direction) that are subjected to prestressing and arbitrary magnetic fields and (b) the continuum modeling of these materials using transversely isotropic energy functions.