The research presented in this dissertation pertains to the evaluation of stiffness of carbon nanotubes (CNTs) in a multiscale framework and modeling of the interfacial mechanical behavior in CNT-polymer nanocomposites. The goal is to study the mechanical behavior of CNTs and CNT-polymer interfaces at the atomic level, and utilize this information to develop predictive capabilities of material behavior at the macroscale. Stiffness of CNTs is analyzed through quantum mechanical (QM) calculations while the CNT-polymer interface is examined using molecular dynamics (MD) simulations. CNT-polymer-matrix composites exhibit promising properties as structural materials and constitutive models are sought to predict their macroscale behavior. The reliability of determining the homogenized response of such materials depends upon the ability to accurately capture the interfacial behavior between the nanotubes and the polymer matrix. In the proposed work, atomistic methods are be used to investigate the behavior of the interface by utilizing appropriately chosen atomistic representative volume elements (RVEs). Atomistic simulations are conducted on the RVEs to study mechanical separation with and without covalent functionalization between the polymeric matrix and two filler materials, namely graphite and a (12,0) Single Wall zig zag CNT. The information obtained from atomistic studies of separation is applicable for higher level length scale models as cohesive zone properties. The results of the present research have been correlated with available experimental data from characterization efforts.