Tissue engineering strategies require the provision of a micromechanical state of stress that is conducive to the generation and maintenance of healthy mature tissue. Of particular interest, angle-ply biomimetic scaffolds augmented with cellular content have been proposed for annulus fibrosus (AF) engineering in order to repair the intervertebral disc. However, the influence of the inherent variability of fabricated constructs and physiological conditions on overall scaffold mechanics, micromechanical environment within the scaffold, and consequent cellular differentiation is relatively unknown. In this study, melt extrusion 3D fiber-deposition (3DF) was used to fabricate five different polycaprolactone angle-ply scaffold architectures which were subject to multiaxial tensile testing and linear elastic orthotropic constitutive fitting. All scaffold groups predicted stiffnesses similar to previously reported native AF moduli in biaxial and uniaxial tensile strain. However, no single scaffold group in this study simultaneously achieved all target AF mechanics in all loading regimes. In equibiaxial tension, the biaxial stiffness ratio of native AF (EEr = 0.55 to 0.62) was predicted between fiber angles of 30° and 35°, which is similar to the collagen orientation in native AF. In global equibiaxial loading, an apparent asymptote in the transverse moduli (EEx ranging −380 MPa to 700 MPa) was observed near the 40° fiber angle scaffolds in equibiaxial tensile strain, attributed to stiffening from the transverse loading. These results highlight that tissue engineering scaffold designs should target replication of physiologically-relevant native tissue mechanics and demonstrate the importance of designing constructs that are unaffected by anticipated variations in manufacturing and clinical application.