The heterogeneous composition, collagen fiber organization and mechanical properties of the supraspinatus tendon (SST) offer an opportunity for studying the structure-function relationships of fibrous musculoskeletal connective tissues. The objective of this study was to evaluate the contribution of collagen fiber organization to the planar tensile mechanics of the human SST. This was accomplished by fitting biaxial tensile data with a structural constitutive model that incorporates a sample-specific angular distribution of nonlinear fibers. Biaxial testing was employed to avoid the limitation of non-physiologic traction-free boundary conditions present during uniaxial testing. Samples were tested under a range of boundary conditions with simultaneous monitoring of collagen fiber orientation via polarized light imaging. The experimental data were input into a hyperelastic constitutive model incorporating the contributions of the uncrimped fibers. The model fit the longitudinal stresses well and was successfully validated. The transverse stresses were fit less well with greater errors observed for less aligned samples. Additional strain energy terms representing fiber-fiber interactions are likely necessary to provide closer approximation of the transverse stresses. This approach demonstrated that the longitudinal tensile mechanics of the SST are primarily dependent on the moduli, crimp, and angular distribution of its collagen fibers.