The lattice vibration of ${\mathrm{YBa}}_{2}$${\mathrm{Cu}}_{3}$${\mathrm{O}}_{7}$ is investigated based on a distributed-multipole model. In this model, the interatomic potential is expressed by means of a multipole-multipole interaction. The dipole and quadrupole moments are taken into account as higher-order multipole moments in order to include structural anisotropy in ${\mathrm{YBa}}_{2}$${\mathrm{Cu}}_{3}$${\mathrm{O}}_{7}$. The quadrupole moments, as compared with the dipole moments, play an important role in the structural stability of this material. The phonon-dispersion relation and the density of states are calculated. The obtained neutron-weighted density of states gives good agreement with the experimental phonon spectrum. The relation between the vibrational properties of the oxygen atoms and the structural a-b anisotropy is discussed.