The mechanical properties of super carbon tubes, a recently developed network material made by conjoined single-walled carbon nanotubes, are studied via molecular dynamics simulations. It is found that such tubes have some unusual properties distinctly different from both individual and bundled carbon nanotubes. The rupture strains of super carbon tubes can reach up to 31-47%, several times higher than that of single-walled carbon nanotubes. Their mechanical behavior is sensitively dependent on both the chiral vectors of the first- and the second-level structures, as well as the inter-junction distance. The hierarchical structure plays a dominant role in the deformation and rupture behavior of super carbon tubes. Owing to their unique and superior properties, super carbon tubes might be used as novel materials with extremely low mass density, high strength and high flexibility, which are of extensive interest in a broad range of technologically important applications.