The aim of this article is to present one more possible derivation of the Einstein's equations of general relativity. The new route is based on old concepts of continuum mechanics, extended to four spacetime dimensions. Our main idea is to consider Einstein's equations as the constitutive relations of the spacetime manifold. Moreover, for us, the spacetime manifold is a nonlinear elastic medium with extrinsic defects (extra-matter). This idea dates back to Cauchy's treatment of elasticity. In Cauchy's words: “the crucial ingredient in solid mechanics is the equation which expresses how the force intensity at any point in a body is related to the change of shape near that point.” We will try to generalize them.