The mechanical state strongly influences the magnetic response of ferromagnetic materials. In this paper, the effect of time-varying mechanical stresses on magnetic behavior is modeled by combining a vector-play model and a multiscale approach. The approach incorporates the influence of the crystallographic texture. The model is applied to a polycrystalline low-carbon steel (DC04). Uniaxial measurements are used to identify the dissipation parameters. The model is further validated under complex uniaxial magneto-elastic loading conditions, different from those used for parameter identification, including simultaneous variations of magnetic field and stress. To the best of our knowledge, the proposed approach is the first multiaxial magneto-elastic hysteresis model able to describe the response of a magnetic material to simultaneously varying magnetic field and stress and validated under such loading conditions.