Nanostructures such as carbon nanotubes have a broad range of potential applications such as nanomotors, nano-oscillators and electromechanical nanothermometers, and a proper understanding of the molecular interaction between nanostructures is fundamentally important for these applications. In this paper, we determine the molecular interaction potential of interacting carbon nanotubes for two configurations. The first is a shuttle configuration involving a short outer tube sliding on a fixed inner tube, and the second involves a telescopic configuration for which an inner tube moves both in the region between two outer tubes and through the tubes themselves. For the first configuration we examine two cases of semi-infinite and finite inner carbon nanotubes. We employ the continuum approximation and the 6–12 Lennard-Jones potential for non-bonded molecules to determine the molecular interaction potential and the resulting van der Waals force, and we evaluate the resulting surface integrals numerically. We also investigate the acceptance condition and suction energy for the first configuration. Our results show that for the shuttle configuration with a semi-infinite inner tube, the suction energy is maximum when the difference between the outer and inner tubes radii is approximately 3.4 Å, which is the ideal inter-wall spacing between graphene sheets. For the finite inner tube, the potential energy is dependent on both the inner and outer tube lengths as well as on the inter-wall spacing. In terms of the oscillating frequency, the critical issue is the length of the moving outer tube, and the shorter the length, the higher the frequency. Further, for the telescopic configuration with two semi-infinite outer nanotubes of different radii, we find that the interaction energy also depends on the difference of the tube radii. For two outer nanotubes of equal radii we observe that the shorter the distance between the two outer nanotubes, the higher the magnitude of the interaction potential around the origin.