Great efficiency to penetrate into living cells is attributed to carbon nanotubes due to a number of direct and indirect observations of carbon nanotubes inside the cells. However, a direct evidence of physical translocation of nanotubes through phospholipid bilayers and the exact microscopic mechanism of their penetration into cells are still lacking. In order to test one of the inferred translocation mechanisms, namely the spontaneous piercing through the membrane induced only by thermal motion, we calculate the energy cost associated with the insertion of a carbon nanotube into a model phospholipid bilayer using the single-chain mean field theory, which is particularly suitable for the accurate measurements of equilibrium free energies. We find that the energy cost of the bilayer rupture is quite high compared to that of the energy of thermal motion. This conclusion may indirectly support other energy-dependent translocation mechanisms, such as, for example, endocytosis.