The response of wall stress to the elasticity of each layer in the aorta wall was investigated to understand the role of the different elastic properties of layers in the aortic dissection. The complex mechanical interaction between blood flow and wall dynamics in a three-dimensional arch model of an aorta was studied by means of computational coupled fluid-structure interaction analysis. The results show that stresses in the media layer are highest in three layers and that shear stress is concentrated in the media layer near to the adventitia layer. Hence, the difference in the elastic properties of the layers could be responsible for the pathological state in which a tear splits across the tunica media to near to the tunica adventitia and the dissection spreads along the laminar planes of the media layer where it is near the adventitia layer.