The buckling behavior of cross-linked functionalized carbon nanotubes (CNTs) with polyethylene (PE) chains under physical adsorption of polymers (cfCNTs/polymer) is studied by classical molecular dynamics (MD) simulations, and the results are compared with those for the pure CNTs under the physical adsorption of polymers. Considering non-covalent functionalization, the effect of type of functional group, i.e. aramid and PE chains, on the interactions between polymers and cfCNTs is investigated. Based on the results, the gyration radius of cfCNTs/polymer increases by raising the weight percentage of non-covalent polymer chains. Also, the simulation results for most cases demonstrate that the gyration radius of cfCNTs/polymer is larger than that of pure CNTs/polymer for the similar weight percentage of non-covalent polymer chains. Moreover, the critical buckling force and the critical buckling strain of the cfCNTs/polymer are lower than those of pure CNT/polymer for the similar weight percentage of non-covalent polymer chains, although some exceptions can be observed. Besides, by raising the weight percentage of non-covalent polymer chains, the critical buckling force cfCNTs/polymer increases for a specific weight percentage of cross-linked PE chains.