A computational strategy to predict the elastic properties of carbon nanotube-reinforced polymer composites is proposed in this two-part paper. In Part I, the micro-structural characteristics of these nano-composites are discerned. These characteristics include networks/agglomerations of carbon nanotubes and thick polymer interphase regions between the nanotubes and the surrounding matrix. An algorithm is presented to construct three-dimensional geometric models with large amounts of randomly dispersed and aggregated nanotubes. The effects of the distribution of the nanotubes and the thickness of the interphase regions on the concentration of the interphase regions are demonstrated with numerical results. © 2013 Elsevier B.V. All rights reserved.