A series of pressurization and tensile loading experiments on mouse carotid arteries is performed with deformation measurements acquired during each experiment using three-dimensional digital image correlation. Using a combination of finite element analysis and a microstructure-based constitutive model to describe the response of biological tissue, the measured surface strains during pressurization, and the average axial strains during tensile loading, an inverse procedure is used to identify the optimal constitutive parameters for the mouse carotid artery. The results demonstrate that surface strain measurements can be combined with computational methods to identify material properties in a vascular tissue. Additional computational studies using the optimal material parameters for the mouse carotid artery are discussed with emphasis on the significance of the qualitative trends observed.