This work is focused on the synthesis, characterization and computational studies of multiwall carbon nanotubes. Growth of pure carbon nanotubes have been carried out by vapor phase growth and thermal CVD methods. After optimizing the growth parameters for both methods, the multi-walled carbon nanotubes (MWCNTs) have been obtained. Best optimized temperatures are 900oC and 825oC for vapor phase growth and thermal CVD methods respectively, showing highest yield of CNTs. Average length of CNTs is around 72ìm for acetylene method, and 60ìm for xylene method for diameters range of 30-50nm. In the second stage, by using the geometrical parameters of the experimental observations, computational studies of CNTs are carried out to know the elastic bending and buckling behaviors of carbon nanotubes. A Finite Element (FE) approach has been made to analyze and study the bending deformations and buckling behavior of MWCNTs. The results calculated in this work, agree with the results of other similar numerical simulation studies available in the literature and then establishing the validity of the present FE approach. The results could be an instrument for studying the mechanical behaviors of MWCNTs and their usefulness in nanocomposite materials field. It can be used as a substitute competent method to study bending and buckling of the CNTs accurately.