The promise of enhanced and tailored properties motivates the study of one-dimensional nanomaterials, especially aligned carbon nanotubes (A-CNTs), for the reinforcement of polymeric materials. While CNTs have remarkable theoretical properties, previous work on aligned CNT polymer matrix nanocomposites (A-PNCs) reported mechanical properties that are orders of magnitude lower than those predicted by rule of mixtures. This large difference primarily originates from the morphology of the CNTs, because the CNTs that comprise the A-PNCs have significant local curvature commonly referred to as waviness. Here we present a simulation framework capable of analyzing 10 5 wavy CNTs with realistic three-dimensional morphologies to quantify the impact of waviness on the effective elastic modulus contribution of wavy CNTs. The simulation results show that due to the low shear modulus of the reinforcing CNT'fibers', and large () compliance contribution of the shear deformation mode, waviness reduces the effective stiffness contribution of the A-CNTs by two to three orders of magnitude. Also, the mechanical property predictions resulting from the simulation framework outperform those previously reported using finite element analysis since representative descriptions of the morphology are required to accurately predict properties of the A-PNCs. Further work to quantify the morphology of A-PNCs in three-dimensions, simulate their full non-isotropic constitutive relations, and predict their failure mechanisms is planned.