Carbon nanotubes (CNTs) are considered to be one of the contemporary materials exhibiting superior mechanical, thermal and electrical properties. A new generation state-of-the-art composite material, carbon nanotube reinforced polymer (CNTRP), utilizes carbon nanotubes as the reinforcing fibre element. CNTRPs are highly promising composite materials possessing the potential to be used in various areas such as automotive, aerospace, defence, and energy sectors. The CNTRP composite owes its frontline mechanical material properties mainly to the improvement provided by the CNT filler. There are challenging issues regarding CNTRPs such as determination of material properties, and effect of chirality and size on the mechanical material properties of carbon nanotube fibres, which warrant development of computational models. Along with the difficulties associated with experimentation on CNTs, there is paucity in the literature on the effects of chirality and size on the mechanical properties of CNTs. Insight into the aforementioned issues may be brought through computational modelling time- and cost-effectively when compared to experimentation. This study aims to investigate the effect of chirality and size of single-walled carbon nanotubes (SWNTs) on its mechanical material properties so that their contribution to the mechanical properties of CNTRP composite may be understood more clearly. Nonlinear finite element models based on molecular mechanics using various element types substituting C-C bond are generated to develop zigzag, armchair and chiral SWNTs over a range of diameters. The predictions collected from simulations are compared to the experimental and computational studies available in the literature.