In this paper, the buckling response of single-walled carbon nanotube (SWCNT)-reinforced shape memory polymer nanocomposite beams is investigated through a computational multiscale approach. First, the Mori-Tanaka micromechanical model is used to extract the effective mechanical properties of SWCNT-polymer nanocomposites. The role of interfacial region between the nanotubes and polymer matrix in the elastic properties is taken into account in the analysis. Then, the buckling behavior of the nanocomposite beams is evaluated by the finite element method (FEM). The effects of nanotube content, interphase and temperature on the buckling response are investigated. It is observed that the addition of SWCNT into the polymeric materials increases the buckling capacity of the resulting nanocomposite beams. According to the results, the buckling characteristics of shape memory polymer nanocomposite beams are affected by the CNT/polymer interphase. The increase of temperature significantly decreases the buckling loads of nanocomposite beams due to the decrease of nanocomposite elastic modulus.