Abstract: Investigation of the consequence of large deformation of blood vessel due to change in transmural pressure is crucial to the understanding of vein graft or other surgical operations involving blood vessel. The paper proposes and verifies new constitutive laws describing nonlinear stress-strain relation of orthogonal anisotropic materials. It can be used for large deformation calculation of blood vessels in the bio-mechanics regime. The derivation of the constitutive law is pure mathematical reasoning based on only one assumption that the stress-strain relation takes a polynomial form. Application is made in a blood vessel test. The correlation between the proposed formula and experimental data is excellent and better than that of the existing exponential expressions