The heterogeneous composition and mechanical properties of the supraspinatus tendon offer an opportunity for studying the structure-function relationships of fibrous musculoskeletal connective tissues. Previous uniaxial testing has demonstrated a correlation between the collagen fiber angle distribution and tendon mechanics in response to tensile loading both parallel and transverse to the tendon longitudinal axis. However, the planar mechanics of the supraspinatus tendon may be more appropriately characterized through biaxial tensile testing, which avoids the limitation of nonphysiologic traction-free boundary conditions present during uniaxial testing. Combined with a structural constitutive model, biaxial testing can help identify the specific structural mechanisms underlying the tendon’s two-dimensional mechanical behavior. Therefore, the objective of this study was to evaluate the contribution of collagen fiber organization to the planar tensile mechanics of the human supraspinatus tendon by fitting biaxial tensile data with a structural constitutive model that incorporates a sample-specific angular distribution of nonlinear fibers. Regional samples were tested under several biaxial boundary conditions while simultaneously measuring the collagen fiber orientations via polarized light imaging. The histograms of fiber angles were fit with a von Mises probability distribution and input into a hyperelastic constitutive model incorporating the contributions of the uncrimped fibers. Samples with a wide fiber angle distribution produced greater transverse stresses than more highly aligned samples. The structural model fit the longitudinal stresses well (median R2 ≥ 0.96) and was validated by successfully predicting the stress response to a mechanical protocol not used for parameter estimation. The transverse stresses were fit less well with greater errors observed for less aligned samples. Sensitivity analyses and relatively affine fiber kinematics suggest that these errors are not due to inaccuracies in measuring the collagen fiber organization. More likely, additional strain energy terms representing fiber-fiber interactions are necessary to provide a closer approximation of the transverse stresses. Nevertheless, this approach demonstrated that the longitudinal tensile mechanics of the supraspinatus tendon are primarily dependent on the moduli, crimp, and angular distribution of its collagen fibers. These results add to the existing knowledge of structure-function relationships in fibrous musculoskeletal tissue, which is valuable for understanding the etiology of degenerative disease, developing effective tissue engineering design strategies, and predicting outcomes of tissue repair.