  We show that spin-orbit interaction and elastic spin-Hall effect can exist in
a classical mechanical system consisting of a two-dimensional honeycomb lattice
of masses and springs. The band structure shows the presence of splitting at K
point induced by the difference of longitudinal and transverse elastic
constant, and this splitting can be regarded as an effective Dresselhaus-type
spin-orbit coupling. Interestingly, as an initial displacement away from the
equilibrium is applied, the time evolution simulation shows that waves of
different spin polarization propagates along different directions at the Gamma
and K point, which is characteristic of spin-Hall effect. Several cases for
spin-Hall effect are also discussed.
