We employed first‐principles simulations using a hybrid exchange‐correlation density functional PBE0 within an LCAO approximation to investigate the properties of InS single layers and nanotubes constructed from its stable orthorhombic and hypothetical hexagonal phases. We have found two types of 4‐plane layers with relatively low formation energy, Rec4 and Hex4, which have been extracted from the orthorhombic and hexagonal phases, respectively. By rolling up Rec4 and Hex4 layers, the initial structures of single‐ and double‐walled nanotubes have been generated. The nanotube formation and strain energies calculated after atomic relaxation show that the most stable structures can be obtained from the rectangular Rec4 nanosheets. At the same time, the double‐walled nanotubes folded from the Rec4 nanosheets may be potentially useful for photocatalytic water splitting if they can really be synthesized.