Ligaments and tendons undergo volume loss when stretched along the primary fiber axis, which is evident by the large, strain-dependent Poisson’s ratios measured during quasistatic tensile tests. When continuum constitutive models have been used to describe ligament material behavior they have generally assumed incompressibility, which does not reflect the volume loss seen experimentally. We developed a strain energy equation that can predict both the nonlinear, transversely isotropic behavior as well as the large, strain-dependent Poisson’s ratios seen experimentally. This hyperelastic constitutive model was implemented in the finite element solver FEBio and the quasistatic and timedependent material behaviors were compared to a nearly incompressible constitutive model. The new model was able to predict uniaxial stress-strain behavior comparable to the nearly incompressible model and successfully predicted a large, strain-dependent Poisson’s ratio. Biphasic simulations that represented the solid phase with the constitutive model predicted a large outward fluid flux and substantial stress-relaxation, suggesting that the viscoelastic behavior of ligaments and tendons can be predicted by modeling fluid movement when combined with a large Poisson’s ratio.