Low-frequency vibrations below 200cm −1 of crystalline α,α-trehalose dihydrate were observed by far-infrared spectroscopy. Peaks were classified to (1) strong and less sharp and (2) weak and sharp. By density functional theory calculations, two strong peaks at 67.7 and 75.9cm −1 are assigned to the torsion modes of two hydroxymethyl groups combined with the hydrogen torsional motion of two water molecules. A sharp peak at 49.3cm −1 appearing at 4K is assigned to the translational motion of water molecule. Several sharp peaks of single crystal sample below 60cm −1 showed polarization dependence at 4K.