The conformational studies of the torsional, tensile and bending flexibility of DNA within the B-family of forms are reviewed. The calculated values are in agreement with the experimental data. It means that the basic mechanism of the double helix elasticity descends from the small amplitude torsional vibrations of atoms. The torsional flexibility of B-DNA depends on the nucleotide sequence, namely poly(dA) . poly(dT) is stiffer than poly(dG) . poly(dC) due to the interactions between methyl groups of thymines and (C2(1) H2-groups of the neighbouring sugar rings. It is found that the B leads to A transition increases the torsional stiffness of the double helix as well. Possible correlation between conformational changes in the adjacent nucleotides is discussed. The crystalline structure of the dodecamer CGCGAATTCGCG testifies to the anisotropic flexibility of DNA and confirms the model for DNA folding in the nucleosome by virtue of "mini-kinks". The bending stiffness of DNA presumably depends on the base sequence: purine-pyrimidine dimers prefer bending into the minor groove, while pyrimidine-purine dinucleotides are more easily bent into the major one. Fluctuations in B-DNA are compared with those in alpha-helix.