Mouse models of Marfan Syndrome (MFS) provide insight into the type and extent of vascular abnormalities manifested in this disease. Inclusion of the mgR mutation causes the otherwise normal extracellular matrix glycoprotein fibrillin-1 to be under-expressed at 15–25% of its normal level, a condition seen in MFS. Aortas in patients with MFS are generally less distensible and may experience dissecting aneurysms that lead to premature death, yet little is known about effects on other large arteries. In this study, common carotid arteries from mice heterozygous (R/+) and homozygous (R/R) for the mgR mutation were studied under biaxial loading and compared to results from wild-type controls (+/+). Carotids from +/+ and R/+ mice exhibited similar biomechanical behaviors whereas those from R/R mice were slightly stiffer in the circumferential direction while dramatically different in the axial direction. That is, R/R carotids were stiffer axially and had lower in vivo axial prestretches. Biaxial stress–stretch data were fit with a four-fiber family constitutive model. The fitted data yielded a lower value of an isotropic parameter for the R/R carotids, which reflects a compromised elastin-dominated amorphous matrix. Overall, it appeared that changes in axial mechanical properties afforded R/R carotids a means to compensate, at least early in maturity (9 weeks of age), for the loss of an important structural constituent as they attempted to maintain structural integrity in response to normal mean arterial pressures and thereby maintain mechanical homeostasis.