The ideal (theoretical) strength was originally defined as the stress or strain at which perfect crystal lattice became mechanically unstable with respect to arbitrary homogeneous infinitesimal deformation. This has been intensely investigated because the ultimate strength without defects is a fundamental mechanical characteristic of materials. In the analyses, the instability criteria have been studied on the basis of elastic constants. Recent developments in computational technology make it possible to analyze the ideal strength on the basis of quantum mechanics. On the other hand, it is well known that the mechanical strength of components is dependent not only on (1) material (atom species), but also on (2) loading condition and (3) structure. Because most studies on the strength in terms of atomic mechanics have focused on the factor (1) (materials), analysis has mainly been conducted on simple crystal consisting of perfect lattices (e.g. fcc and bcc) under simple loading conditions (e.g. tension), though some have explored the properties of bulk materials with defects (e.g. vacancy and grain boundary). Small atomic components (nano-structured components) such as nano-films, nano-wires (tubes) and nano-dots (clusters) possess their own beautiful, defect-free structures, namely ideal structure. Thus, they show characteristic high strength. Moreover, utilizing the structure at the nanometer or micron level is a key technology in the development of electronic devices and elements of micro (nano) electro-mechanical systems (MEMS/NEMS). Therefore, it is important to understand the mechanical properties not only for the sake of scientific interest, but also for engineering usefulness such as design of fabrication/assembly processes and reliability in service. In the other words, the effects of structure (factor (3); e.g. film/wire/dot) have to be understood as the basic properties of atomic components. Thus, the definition of ideal strength should be expanded to include the strength at instability of components with ideal structures under various external loads (factor (2)), which provides fundamental knowledge of nano-structured materials. In this paper, we review works on the strength of ideal nano-structured components in terms of factor (3), mainly under tension.