In this study, the ferroelectric properties and its coupling behavior with mechanical strain of ultrathin PbTiO3 nanotubes are investigated by first-principles calculations. The nanotube possesses spontaneous polarization despite their sidewalls being thinner than the critical thickness at which the thin lms lose ferroelectricity; this indicates the absence of an intrinsic critical size for ferroelectricity. The ground state of the nanotube is not purely FE since it primarily involves antiferrodistortive (AFD) rotations of oxygen atoms due to compression in the inner tube wall. The emergence of the AFD displacement plays a central role in stabilizing both the nanotubular structure and FE distortions due to direct AFD-FE coupling. Moreover, we predict intriguing rich phase transitions due to axial strains including polarization vortices as an important class of nanoscale FE ordering. Finally, the mechanical strength of PbTiO3 nanotube is evaluated, and the critical stresses under the tension and compression states are obtained.