Internal pressure in the healthy human annulus fibrosus leads to multiaxial stress in vivo, yet uniaxial tests have been used exclusively to characterize its in vitro mechanical response and to determine its elastic strain energy function (W). We expected that biaxial tension tests would provide unique and necessary data for characterizing the annular material response, and thereby, for determining W. We performed uniaxial and biaxial tests on specimens of annulus, then developed an objective methodology for defining an appropriate form for W that considers data from multiple experiments simultaneously and allows the data to dictate more directly the form and the number of parameters needed. We found that the stresses attained in the biaxial tests were higher, while the strains were considerably lower, than those observed in the uniaxial tests. A comparison of strain energy functions determined from the different data sets demonstrated that constitutive models derived from uniaxial data could not predict annulus behavior in biaxial tension and vice versa. Since the annulus is in a state of multaxial stress in vivo, we conclude that uniaxial tests alone are insufficient to prescribe a physiologically relevant W for this tissue.