Tailorable anisotropic intrinsic and scale-dependent properties of carbon nanotubes (CNTs) make them attractive elements in next-generation advanced materials. However, in order to model and predict the behavior of CNTs in macroscopic architectures, mechanical constitutive relations must be evaluated. This study presents the full stiffness tensor for aligned CNT-reinforced polymers as a function of the CNT packing (up to similar to 20 vol. %), revealing noticeable anisotropy. Finite element models reveal that the usually neglected CNT waviness dictates the degree of anisotropy and packing dependence of the mechanical behavior, rather than any of the usually cited aggregation or polymer interphase mechanisms. Combined with extensive morphology characterization, this work enables the evaluation of structure-property relations for such materials, enabling design of aligned CNT material architectures. (C) 2013 AIP Publishing LLC.