Relaxed force constants (RFC) and vibrational root-mean-square (VRMS) deviations are used for comparative characterization of mechanical properties of canonical 2'-deoxyribonucleosides (2DRs) and 1,2-dideoxyribose molecule, their model sugar residue. It has been shown that RFC and VRMS should be preferred over traditional force constants when one needs to obtain the quantitative measure of the 'collective' parameter flexibility (furanose sugar pseudorotation phase P in particular) and compare it with classical torsion angles (β, γ, ε, χ). It has been found that torsions ε and β determining the 2DRs backbone hydroxyl orientations are as soft as the pseudorotation phase P with RFC values within 1-10 kcal mol(-1) rad(-2) depending on conformation. Torsion γ is the most rigid one with RFC 15-30 kcal mol(-1) rad(-2), while the glycosidic torsion χ is characterized by intermediate values of RFC (typically 5-10 kcal mol(-1) rad(-2)) and its RFC changes by 10 times, depending on the furanose sugar conformation (K(χ)≈ 3 kcal mol(-1) rad(-2) in B- vs. K(χ)≈ 21 kcal mol(-1) rad(-2) in A-DNA-like conformation of 2'-deoxycytidine). Quantum zero-point motion of the nuclei makes the dominant contribution to VRMS deviations of molecules structural parameters: 9-22° for β, ε and P, 5-7° for γ and χ at the temperature of 0 K, and 15-38° for β, ε and P, 9-26° for γ and χ at the room temperature (298.15 K). Obtained results can be used in constructing simple dynamical models of the DNA fragments.