© 2015, Pleiades Publishing, Ltd.Temperature dependence of the Young’s modulus of cylindrical single-wall nanotubes with zigzag and armchair chiralities and consolidated-wall nanotubes has been studied by the molecular mechanics method with the use of the atom–atom potential. The nanotubes have been obtained by rolling up of crystal layers (111) of TiO2 with fluorite structure. Calculations have been performed for isothermal conditions on the basis of calculating the Helmholtz free energy of the system. The dependence of the Helmholtz free energy of nanotubes on the period has been calculated in the quasi-harmonic approximation as a result of calculation of phonon frequencies. It has been shown that the temperature dependence of the stiffness of nanotubes is determined by their chirality, and some nanotubes exibit anomalous behavior of both the Young’s modulus and the period of unit cell with variation in temperature.