In this paper, the anti-plane shear motion of an asymmetric
three-layered inhomogeneous elastic plate has been examined. An
asymptotic approach is employed for the present investigation. Both the
generalized and unified dispersion relations within the long-wave
low-frequency range have been determined. The obtained unified
dispersion relation is investigated taking into account the recently
analyzed material contrast for layered plate with mixed stiff-soft
layers of different material properties. Finally, we make comparison
with symmetric plate being a special case of the asymmetric plate under
consideration in the end.