The structral members like beams and plates are often subjected a mode of sudden failure due to high compressive load which is charecterised as buckling. The buckling behaviour is one of the most important parameters needs to be considered while desingnig the structural members like beams. This paper studies the buckling behaviour of Carbon Nanotube (CNT) reinfocreced polymer composite beams by using Classical Laminate Plate Theory (CLPT) approach. The elastic constants obatained for the CNT reinforced polymer composite by applying Mori-Tanaka method are furthur used to analyse the effect of stacking sequence, CNT Volume fraction in the composite, and CNT radii on the critical buckling loads of an eight layerd nanocomposite beam. The Numerical results are also presentd and compared for various boundary conditionof beams like clamped-clamped and hinged-hinged. The main intension behind this study is to find the suitability of the nanocomposites as stuctural components like air-craft wings and ducts.