In this paper, the effects of nanotube diameter, waviness ratio and wavelength ratio on the tensile elastic modulus (TEM) of the carbon nanotube (CNT) reinforced polymer composites is investigated using a 3-D nanoscale representative volume element (RVE) based on continuum mechanics and using the finite element method (FEM). Formula to extract the effective material constant from solutions for the RVE under axial loading is derived based on the elasticity theory. Both long and short CNT embedded in the matrix are considered for investigating the effect of fiber diameter variation whereas only long wavy CNT is considered for investigating the effect of waviness and wavelength ratio variation, all at a volume fraction of 5%. First, the effects of CNT diameter on the TEM of the composite are investigated. Numerical results show that TEM of the polymer composite is influenced by tube diameter variation for both long and short CNT. Then the effects of waviness ratio and wavelength ratio on the TEM of polymer composite are investigated. Results show that both the waviness and wavelength ratio variation of CNT significantly influence the TEM of the polymer composite.