The surface evolution of an annular tube has been established on the basis of lattice diffusion and linear stability analysis. Without surface disturbance, the annular tube shrinks to reduce the surface energy while the cross-sectional area of the tube remains constant. For an annular tube having infinitesimal thickness, the time dependence of the tube radius follows a linear law. When surface energy is significant, a new dispersion relation describing the morphological stability of crystalline tubes due to longitudinal surface perturbation has been formulated. A criterion has been obtained on the dependence of perturbation growth rate on perturbation frequency. The perturbation will grow when the perturbation frequency is less than the critical frequency, which is equal to the inverse of the inner surface radius. The surface instability leads to the formation of closed end of crystalline tubes. (C) 2004 Elsevier B.V. All rights reserved.