Since the Natural Strain is obtained by integrating an infinitesimal strain increment on an identical line element, this theory has merits that the rigid body rotation can be removed from the rotating angle of a line element and the additive law of strain on an identical line element can be satisfied. Taking the Natural Strain theory into consideration, we investigate the relation between directions of principal axis of stress and strain from experiments in the elastic region by using the specimens, which have already received large multi-axial pre-deformation. In this report, two kinds of different deformation paths, i.e. the simple shear after simple tension and the simple tension after simple shear, are treated as pre-deformation. And, we confirm weather the different deformation history influences on anisotropy of the elastic modulus G.