Effects of dispersion of the fiber orientation on the mechanical property of the arterial wall in health and disease subjected to the combined internal pressure and axial loading are examined within the framework of the finite deformation hyper-elasticity theory. Taking into account the residual stress, a two layer thick-walled circular cylindrical tube model with the fiber-reinforced incompressible composite hyper-elastic material is employed. Stress-radius curves and stress distributions of the arterial wall are given in health and disease considering dispersion of the fiber orientation. With instability/bifurcation analysis, it is found that not only the uniform inflation of the arterial wall in health, but also the instability or bifurcation problem for the arterial wall in disease may be described by this model.