In this paper, using the specimen which is already applied the pre-deformation of a large uni-axial tension, the estimation method for the yield stress when the cyclic loads of uni-axial tension and compression are applied with keeping the constant strain amplitude is described. Based on the Natural Strain theory, the yield stress is estimated by the tangent modulus of the principal deviatoric stress and the principal deviatoric strain curve. Especially, the relations between the change of the yield stress and the number of cycle are examined under the different size of the pre-deformation of uni-axial tension and the different amplitude of strain. Moreover, the results based on this method are compared with the results by conventional proof stress.