The recent developments of lightweight and highly-strong structural materials have resulted in the increased attention paid to the nanocomposites reinforced with Carbon Nanotubes (CNTs), owing to their unique mechanical properties. This paper explores the stability analysis of the nanocomposite beams reinforced with CNTs via a computational model based on the finite element method. The properties of the nanocomposite material are determined with the help of the Mori-Tanaka micromechanical approach where various types of CNT dispersion, such as aligned and random distribution, are taken into account. Moreover, the effects of weak Van der Waals interaction in the CNT-matrix interface are taken into consideration. The influence of some important design parameters like the volume fraction of CNT, diameter of nanotubes, thermal condition, interfacial interphase thickness, and geometry of the beam cross-section is examined regarding the influence of these parameters on the critical buckling capacity. The results reveal that increasing the volume fraction of CNT significantly enhances the stiffness of the material, making it highly resistant to elastic instability. Additionally, the presence of the interfacial interphase layer plays a significant role in improving the performance of the structure. It is concluded from the numerical analysis that the temperature rise has a negative impact on the buckling behavior since the effective stiffness of the nanocomposites decreases. In addition, it has been found out that the utilization of CNTs with small diameters and larger interphase thickness leads to higher critical buckling loads especially by considering the interface phenomena. Moreover, it is noted that the beam geometry has a great influence on stability behavior. Thus, the longer beams have lower buckling loads, while the increased cross-sections lead to the improvement of the load-carrying capacity. In addition, it can be stated that the beams with hollow cross-sections have better performance than beams with solid cross-sections. From the mesh analysis, it is shown that there is no significant change in the results after reaching an appropriate number of elements. Therefore, computational cost efficiency can be achieved without losing accuracy.