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There has been increasing attention to utilizing carbon nanotubes (CNTs) as nano-fillers in polymers and polymer matrix composite materials, such as carbon fiber reinforced plastics. However, the understanding of how randomly oriented CNTs affect mechanical properties of such CNT-engineered composites is limited. This paper serves to develop an analytical model for determining the elastic properties of CNT-engineered composite materials using a mechanics of materials approach. Analysis of the properties was constructed progressively using material unit cells starting from the nano level, to the micro level, and finally, to the macro level. MATLAB programming platform was used to facilitate simulation of the modeling process. Typical simulation cases of the CNT-engineered composite materials are presented in comparison with published experimental and other data, where appropriate.