Abstract The super-graphene (SG) and super-square (SS) carbon nanotube network are built by the straight single-walled carbon nanotubes and corresponding junctions. The elastic buckling behaviors of these carbon nanotube networks under different boundary conditions are explored through the molecular structural mechanics method. The following results are obtained: (a) The critical buckling forces of the SG and SS networks decrease as the side lengths or aspect ratios of the networks increase. The continuum plate theory could give good predictions to the buckling of the SS network but not the SG network with non-uniform buckling modes. (b) The carbon nanotube networks are more stable structures than the graphene structures with less carbon atoms.