[en] A solution for the tension and torsion problems for the curvilinearly anisotropic nano/microtubes made of orthorhombic crystals in the framework of the Saint-Venant’s approach is given. We find that the number of partial auxetics among the tubes is twice as frequent among the rectilinearly anisotropic crystals, at the same time about one third of 136 orthorhombic crystals are auxetics. It is shown that the torsion causes extension of the nano/microtubes even in the absence of a longitudinal tensile force. This Poynting’s effect substantially depends on the chiral angle, and in particular, it disappears when the chiral angle vanishes. We also investigate an inverse Poynting’s effect when the extension of the nano/microtubes is accompanied by their twisting. It is shown that the signs of Poynting’s effect and Poisson’s ratio are changed several times with the change of the chiral angle. (paper)