The analytical relation between k-points in the primitive-cell Brillouin zone and reduced supercell Brillouin zone is reported for supercell-zone-folding transformation. Examples are given for symmetry points of square and cubic simple, face-centered and body-centered lattices. The cyclic cluster symmetry is considered as a particular case of supercell-zone-folding transformation. The results of the first principles calculations of LiCl crystal in the supercell model as well as the symmetry of one-electron states are discussed using the supercell-zone-folding concept. The first principles calculations of copper impurity in LiCl crystal are made using different supercells. The site symmetry method is applied to find the space group representations induced by Cl p-states and copper d-states. The zone-folding transformation for the two-dimensional layer unit cell is considered in relation to the single wall nanotubes modeling. The results of zone-folding method application to electron states of WS₂-based nanotubes and to phonon calculations of carbon and ZrS₂-based nanotubes are presented and discussed.