Objective To provide reference for understanding the stress state of the aortic arch，select the appropriate constitutive relation, further analyze the biomechanical properties of human aortic arch so as to offer the biomechanical basis for treating aortic arch in clinic. Method Under two different constraints(the first constraint: the constraint along with the direction of ascending aorta; the second constraint: the ascending aorta could move freely, but the end was closed with a hemisphere), three constitutive relationships (linear constitutive, exponential function constitutive, M-R constitutive) and two loads(10.67 kPa and 26.66 kPa), the circumferential stress on human aortic arch were studied by the finite element method, and the results were also discussed. Results The models under two constraints were established and the contour plot of circumferential stress and its distribution along the arc of aortic arch under two constraints, three constitutive relationships and two loads were obtained respectively. Conclusions The exponential function constitutive model could reflect the mechanical properties of aortic arch more comprehensively and the mechanical properties of aortic arch could be reflected more factually under the second constraint.