Abstract: The first part of this paper proposed and verified new constitutive laws describing nonlinear stress-strain relation of blood vessel. It can be used for large deformation calculation of blood vessels in the biomechanics regime. The correlation between the proposed formula and experimental data is excellent and better than that of the existing exponential expressions. But when the material is high nonlinear, the Taylor expansion may have too many terms. It's very difficult to get the material constants corresponding to those terms. So a correct term is added in this part to decrease the number of the terms.