Along with insights into the potential for graft success, knowledge of biomechanical properties of small diameter tissue-engineered blood vessel (TEBV) will enable designers to tailor the vessels' mechanical response to closer resemble that of native tissue. Composed of two layers that closely mimic the native media and adventitia, a tissue-engineered vascular adventitia (TEVA) is wrapped around a tissue-engineered vascular media (TEVM) to produce a self-assembled tissue-engineered media/adventia (TEVMA). The current study was undertaken to characterize the biaxial biomechanical properties of TEVM, TEVA and TEVMA under physiological pressures as well as characterize the stress-free reference configuration. It was shown that the TEVA had the greatest compliance over the physiological loading range while the TEVM had the lowest compliance. As expected, compliance of the SA-TEBV fell in between with an average compliance of 2.73 MPa(-1). Data were used to identify material parameters for a microstructurally motivated constitutive model. Identified material parameters for the TEVA and TEVM provided a good fit to experimental data with an average coefficient of determination of 0.918 and 0.868, respectively. These material parameters were used to develop a two-layer predictive model for the response of a TEVMA which fit well with experimental data.