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Carbon nanotubes (CNT) are potentially promising fibers for ultra high strength composites. In order to fully har-ness the outstanding mechanical properties of carbon nanotubes as fiber reinforcements, it is essential to understand the nature of load transfer between fiber and matrix under various types of loading conditions that include tension, compression, torsion and a combination thereof. In this paper, we study the compressive behavior (buckling and post-buckling) of carbon nanotubes in the neat form, when they are embedded in polyethylene matrix and with in¬terface chemical modifications using molecular dynamics simulations based on Tersoff–Brenner potential. It is ob¬served that the critical load for buckling increases only very marginally for nanotubes embedded in polythene matrix (with non-bonded interface) compared to neat CNTs. When CNTs are chemically bonded to the matrix, the compres¬sive behavior occurs in two phases; pre- and post-buckling phases. First, the critical stress for buckling is found to re¬duce because the change in chemical bonding induces deviation from perfect cylindrical structure. In the post-buck¬ling phase, however, the nanotubes behave similar to short fibers and deform by crushing. The results are compared with continuum solutions, wherever applicable. It is shown that the continuum solutions should be applied carefully whenever the effect of nanoscale interfaces becomes a factor.