Mesoscopic tubular potential is developed for the description of the van der Waals interaction between straight single-walled carbon nanotubes (CNTs) of arbitrary length and orientation. The potential is formulated within a general continuum description of the van der Waals intertube interactions based on the integration of an interatomic potential over the surfaces of the interacting nanotubes. The tubular potential reduces the functional dependence of the potential energy of the interacting nanotubes on six independent geometric variables to a combination of several functions, each depending on only one or two geometric parameters. The parametrization of the tubular potential is based on the carbon−carbon interatomic potential describing nonbonding interactions in graphitic structures. An application of the tubular potential for analytical analysis of the interaction between two CNTs reveals the conditions and driving forces responsible for the alignment of nanotubes and generation of CNT bundles. First mesoscopic simulations, performed with the tubular potential for a system consisting of thousands of nanotubes and having dimensions on the order of a micrometer, predict a spontaneous self-assembly of nanotubes into a continuous network of bundles with partial hexagonal ordering of CNTs in the bundles. The structures produced in the simulations are similar to the structures of CNT films and mats observed in experiments. The general procedure used in the design of the tubular potential is not limited to single-walled CNTs or other graphitic structures and can be extended to a diverse range of systems consisting of various types of nano- and microtubular elements, such as nanotubes, nanorodes, and microfibers, providing new opportunities for mesoscopic modeling of complex nanocomposite materials.