Accurate modeling of the coupling between mechanical and magnetic behavior is a key challenge for designing many electromagnetic devices. The requirements for such modeling are notably the ability to consider multiaxial configurations, thermodynamic consistency to allow the calculation of losses, and the implementability into structural analysis tools. So far, the modeling approaches available in the literature do not usually combine these three features simultaneously. In this paper, for the first time, the influence of mechanical stress on the magnetic hysteretic behavior is modeled through the association of a reversible simplified multiscale approach and a macroscopic energy-based magnetic hysteresis model in a vector-play form. A phenomenological description of the dissipation parameters under mechanical stress is proposed. The non-monotonic effect of tensile stress on the magnetic permeability is modeled using a second-order development in the magneto-elastic energy. Material parameters for both reversible and irreversible behavior are identified from experimental characterization under mechanical stress performed on a DC04 electrical steel. The experimental tests include anhysteretic and hysteretic measurements. Modeling results of the anhysteretic magnetic permeability, the coercive field, and the remanent induction under several levels of peak magnetic field and uniaxial mechanical stress are satisfactorily compared with those obtained experimentally. The model is shown to reasonably predict the hysteresis losses under tensile and compressive stress, as well as the response of the material under a complex magnetic field waveform with harmonic content.