Recent biomimetic design, using multi-walled carbon nanotubes, showed that the synthetic gecko foot hairs have much stronger adhesive strength than natural ones. In this work, an exact continuum elastica model is proposed to study the peeling process of carbon nanotubes from rigid smooth substrates. It has been found that the van der Waals interaction between the tube and the substrate is related to the tube's vertical displacement as well as the bending angle. Numerical simulations reveal that the peeling process is complex, and sometimes includes sudden transitions between different geometric configurations of the nanotube and equilibrium path branch-switching phenomena. The bending angle plays an important part on the peeling force when the tube's radius and the rotation angle in the adhesion region are both large. (C) Koninklijke Brill NV, Leiden, 2011