The arterial wall is a structurally complex material, exhibiting both nonlinearity and anisotropy in its mechanics, with the compelling consequence that the end plate force in a pressure-stretch experiment can increase or decrease with pressure depending on the axial stretch of the vessel. Furthermore, it has long been observed that the axial stretch at which the ex vivo pressure-force curve is flat is close to the in vivo axial stretch, but the mechanism driving this phenomenon has remained unclear. By employing and modifying a custom plugin that represents tissue components as networks, we computationally tested the hypothesis that tensional homeostasis at the microscopic scale could lead to the macroscopic pressure-invariant axial force effect observed at in vivo axial stretch. Our findings suggest that remodeling events for individual fibers to achieve a target stress can, acting in aggregate, cause the vessel to exhibit a pressure-invariant axial force in the pressure-force experiment without any explicit sensing of the pressure-force behavior during remodeling. Computational isolation of tissue components suggested that remodeling of collagen fibers is a primary driver of this result. Further as long seen experimentally, the pressure-force curve plateau occurred at stretches close to the in vivo remodeling stretch.