Varying experimental results on the mechanical properties of carbon nanotube reinforced polymer composites (CNTRPs) have been reported due to the complexities associated with the characterization of material properties in nano-scale. Insight into the issues associated with CNTRPs may be brought through computational techniques time- and cost-effectively. In this study, finite element models are generated in which single walled carbon nanotube models are embedded into the epoxy resin. For modelling interface regions, two approaches named as non-bonded interactions and perfect bonding model are utilized and compared against each other. Representative volume finite element (RVE) models are built for a range of CNTRPs and employed for the evaluation of effects of diameter and chirality on the Young's modulus and Poisson's ratio of CNTRPs, for which there is a paucity in the literature. The outcomes of this study are in good agreement with those reported available in the literature earlier. The proposed modelling approach presents a valuable tool for determining other material properties of CNTRPs.