The first-principles simulations using hybrid exchange-correlation density functional and localized atomic basis set were performed to investigate the properties of CdS nanolayers and nanotubes constructed from wurtzite and zinc blende phases. Different types of cylindrical and facetted nanotubes have been considered. The new classification of the facetted nanotubes is proposed. The stability of CdS nanotubes has been analyzed using formation and strain energies. Obtained results show that facetted tubes are favorable as compared to the most of cylindrical ones. Nevertheless, the cylindrical nanotubes generated from the layers with experimentally proved freestanding existence, also have a chance to be synthesized. Preliminary calculation of facetted nanotubes constructed from the zinc blende phase gives evidence for their possible using in the photocatalytic decomposition of water.