We enhanced a bi-layer fiber-matrix microstructural arterial model with softening and analyzed the artery inflation under the internal pressure. Numerical simulations lead to the following three findings. Firstly, it is found that the fiber strength dominates the strength of the media layer. Secondly, it is found that the strength of the media layer dominates the overall arterial strength and plays the crucial role in the load-bearing capacity of arteries. Thirdly, it is found that residual stresses can increase the overall arterial strength significantly. The pre-existing compression in arteries delays the onset of rupture like the pre-existing compression in the pre-stressed concrete delays the crack opening.