The emergence of carbon nanotubes has brought to light their extraordinary attributes, including remarkable strength, exceptional stiffness, low density, and structural integrity at the nanoscale. These characteristics have ignited enthusiasm for a wide range of technological applications. In the past decade, our comprehension of carbon nanotube mechanics has evolved through a combination of experimental validation, challenging theoretical predictions, and the application of diverse computer simulation techniques. This research endeavors to delve into theoretical predictions concerning the visualization and manipulation of minute structures, with a primary focus on scrutinizing the mechanical characteristics of single-walled carbon nanotubes. The study specifically investigates parameters such as Young's modulus, Poisson's ratio, shear modulus, and buckling criteria across various configurations of these nanotubes. The modeling approach incorporates beam elements to symbolize covalent bonds between Carbon-Carbon (C-C) atoms in Carbon Nanotubes (CNTs). Operational within a continuum mechanics framework, the paper aims to predict the characteristics of these beam elements. Baseline values for C-C bond properties are established through numerical analysis to facilitate simulations. Utilizing a finite element methodology, the paper comprehensively examines the mechanical behavior of carbon nanotubes. Furthermore, a parametric investigation is conducted to evaluate how the diameter of single-walled carbon nanotubes influences shear modulus and buckling loads.