This article describes recent work on mechanics of carbon nanotubes, one of the most fundamental and amazing man-made nanostructures. The noteworthy point is that "nano"-scale mechanics of carbon nanotubes can be well described by the continuum elastic theories for "macro"-scale thin shells. This provides an efficient means to elucidate mechanical deformation effects of carbon nanotubes on their physical and chemical properties, which is significant to develop new-generation nanomaterials based on nanotubes and their composites. Potential applications of the mechanical deformation of nanotubes in nano-electronics and nano-biology are also commented. In addition, theoretical investigations regarding external pressure buckling is carried out here and we have numerically confirmed that larger N (the number of layers) and a smaller D (the innermost diameter) make "corrugation modes" with a larger mode-index k be energetically favored.