The effects of the symmetry breaking on plasmonic properties of metallic non-concentric nanotube dimers are investigated, using the bipolar coordinate system [1]. A general dispersion relation for the coupled surface plasmon modes as function of geometrical characteristics of the system is obtained. In the special case (in the limit of a very large separation between the nanotubes) dispersion relation of the plasmon modes of an isolated symmetry-broken nanotube is derived. Numerical results show the core offset of non-concentric nanotubes leads to the red-shifts of the low energy modes.