Abstract Taking account of two-and three-body interaction of the nearestneighbours, the acoustic modes of NXN square lattice is solved in harmonic approximation. The boundary coupling effect leads to physical pictures of phonons different from those in infinite lattice. The standing wave phonons can only be classified according to space species, and the wave vector losses it’s sense. Numerical computation shows that the strengthening of the covalent property leads to appearance of a boundary coupling soft mode. The modes related to rotation, inner-rotation, C/I structure, and surface wave phonon are also given. The phonon spectrum of finite lattice extends to the lower and higher end. The effects in three dimensions are also considered.