A novel continuum mechanical model of long, flexible, hollow tubes is developed using the Cosserat theory of rods and used to study the mechanics of carbon nanotubes. By adding 'microstructure' to a Cosserat rod, analyses of tubes with deformable cross-sections are permitted. To facilitate the analysis, an approximation is introduced that reduces the infinite number of microstructural degrees of freedom to one complex scalar field. The Cosserat rod and microstructure system is solved both numerically and analytically.