In fact, magnetostriction is more complex and depends on the direction of the crystal axes. In iron, the [100] axes are the directions of easy magnetization, while there is little magnetization along the [111] directions (unless the magnetization becomes close to the saturation magnetization, leading to the change of the domain orientation from [111] to [100]). This magnetic anisotropy pushed authors to define two independent longitudinal magnetostrictions  and .
* In cubic materials, the magnetostriction along any axis can be defined by a known linear combination of these two constants. For instance, the elongation along [110] is a linear combination of  and . 
* Under assumptions of isotropic magnetostriction (i.e. domain magnetization is the same in any crystallographic directions), then  and the linear dependence between the elastic energy and the stress is conserved, . Here, ,  and   are the direction cosines of the domain magnetization, and , , those of the bond directions, towards the crystallographic directions.