Owing to their high aspect ratio, large specific surface area, high axial Young's modulus/strength, and low density, one dimensional carbon nanomaterials can introduce significant change to the mechanical properties of polymer matrices, both static and dynamic. Thus, one of the most important potential applications of carbon nanotubes or nanofibers is to utilize the enhanced dynamic damping properties of polymer nanocomposites for improved vibration, acoustic, and fatigue performances. This study focuses on calculating the nanocomposite energy dissipation under dynamic mechanical loading. A micromechanical model based on quasi-static stick-slip analysis has been developed to quantify the dynamic mechanical properties of the nanocomposites as a function of external strain in the elastic region. Storage and loss moduli are used to characterize such dynamic mechanical behaviors. Influences of nanotube bundling and nanotube alignment on the damping property of composites have been quantified. Simulation results are in good agreement with the reported experimental measurements.