Computational simulations of traumatic brain injury (TBI) are commonly used to advance understanding of the injury–pathology relationship, tissue damage thresholds, and design of protective equipment such as helmets. Both human and animal TBI models have developed substantially over recent decades, partially due to the inclusion of more detailed brain geometry and representation of tissues like cerebral blood vessels. Explicit incorporation of vessels dramatically affects local strain and enables researchers to investigate TBI-induced damage to the vasculature. While some studies have indicated that cerebral arteries are rate-dependent, no published experimentally based, rate-sensitive constitutive models of cerebral arteries exist. In this work, we characterize the mechanical properties of axially failed porcine arteries, both quasi-statically (0.01 s−1) and at high rate (>100 s−1), and propose a rate-sensitive model to fit the data. We find that the quasi-static and high-rate stress–stretch curves become significantly different (p < 0.05) above a stretch of 1.23. We additionally find a significant change in both failure stretch and stress as a result of strain rate. The stress–stretch curve is then modeled as a Holzapfel–Gasser–Ogden material, with a Prony series added to capture the effects of viscoelasticity. Ultimately, this paper demonstrates that rate dependence should be considered in the material properties of cerebral arteries undergoing high strain-rate deformations and provides a ready-to-use model for finite element implementation.