The structure and materials of the blood vessel wall are layered. This article presents the principle of a method to determine the mechanical properties of the different layers in vivo. In vivo measurement begets in vivo data and avoids pitfalls of in vitro tests of dissected specimens. With the proposed method, we can measure vessels of diameters 100 microns and up and obtain data on vascular smooth muscles and adventitia. To derive the full constitutive equations, one must first determine the zero-stress state, obtain the morphometric data on the thicknesses of the layers, and make mechanical measurements in the neighborhood of the zero-stress state. Then eight small perturbation experiments are done on earth blood vessel in vivo to determine eight incremental elastic moduli of the two layers of the blood vessel wall. The calculation requires the morphometric data and the location of the neutral axis. The experiments are simple, the interpretation is definitive, but the analysis is somewhat sophisticated. The method will yield results that are needed to assess the stress and strain in the tissues of the blood vessel. The subject is important because blood vessels remodel themselves significantly and rapidly when their stress and strain deviate from their homeostatic values, and because cell proliferation, differentiation, adhesion, contraction, and locomotion depend on stress and strain in the tissue.