For the first time, the dependences of the strain energy and the band gap of achiral nanotubes obtained by folding monolayers of gallium(II) sulfides and selenides on their diameter have been calculated nonempirically. The calculations were performed using the CRYSTAL17 software package using an atomic basis set within the hybrid density functional theory with a thirteen-percent Hartree–Fock exchange. To take into account the dispersion interactions between the layers in the crystal, the Grimme empirical correction is included in the calculations. As a result of simulation of nanotubes with different chirality and different diameters, the minimum diameters of single-walled nanotubes, at which the integrity of chemical bonds on their outer surface is preserved, are established. It is shown that the dependence of the strain energy on the diameter satisfies the classical law of inverse squares and is the same for nanotubes of the zigzag and armchair types.