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Magnetically induced changes in the velocity of 4.5‐MHz ultrasonic shear waves were investigated in polycrystalline A‐36 steel as a funtion of both uniaxial tensile and compressive stresses. The velocity changes induced by the applied magnetic field exhibit distinctly different stress effects depending on the relative orientations between the shear wave polarization, the magnetic field, and the external stress axis as well as on the magnitude and sign, i.e., tensile or compressive, of the stress. The magnetically induced velocity changes and their stress dependence were found to be insensitive to the elastic anisotropy associated with the preferred orientation (rolling texture). Based on the magnetoelastic coupling in the material, a phenomenological account for the distinctly different stress effects on the magnetically induced velocity changes is given. Good semiquantitative agreement was found between the observed characteristic stress dependence of the magnetically induced velocity changes and the phenomenological explanation presented. The characteristic stress dependence of the magnetically induced velocity change together with its lack of sensitivity to the elastic anisotropy of the material offers a new means of nondestructively determining the magnitude, the direction, as well as the sign of an unknown stress in ferromagnetic materials.