We show a general nonlinear stress-strain response for crystalline materials subject to an initial deformation. The scheme is implemented using 3rd, 4th, and higher order elastic constants. We apply the formulation to a face-centered cubic crystalline Au under shear while in an initially hydrostatically deformed state. We then compare the nonlinear shear stress-strain relations from our derived formulation with Hellmann-Feynman shear stress-strain curves obtained directly from ab initio calculations. The results show that the general analytical expression for the nonlinear stress-strain relation is satisfactory and thus expected to have many applications where ab initio calculations are limited, including cases at finite temperature.