Vertically aligned carbon nanotubes (VACNTs) have been explored widely in various applications due to their unique anisotropic properties. However, its application is limited due to large aspect ratio of nanotubes which lead to buckling phenomena. In this paper, we perform a finite element analysis to predict the variation of elastic modulus and critical buckling load of VACNTs. While elastic modulus is obtained from the slope of stress–strain variation of tubes when one end is fixed and another end is subjected to longitudinal loading, critical buckling load is found using eigenvalue analysis corresponding to first buckling mode. We also perform study to show size dependence of elastic modulus and buckling load of single walled carbon nanotubes (SWCNTs) using FEM approach and compare the results with MD results found in the literature. After validating FEM approach with available results of single-walled and double-walled carbon nanotubes, we apply the same method to arrays of VACNTs. It is found that elastic modulus of VACNTs increases from 1.18 TPa to 2.02 TPa when the size increases from 4 to 36 tubes and then it becomes nearly size independent. The variations of critical buckling load versus other parameters such as tube diameter, intertube spacing, etc., are also obtained. It is found that with the increase in diameter, there is a steep rise in the buckling load for the case of VACNTs arrays. In order to show the influence of non-linear van der Waals force in VACNTs, we compare the above results with and without the presence of van der Waals force and discuss its significance. The modelling and analysis presented in the paper can be used to optimise the number density of VACNTs for different applications. © 2018 Elsevier Ltd