  This paper is concerned with an asymptotic analysis of the dispersion
relation for wave propagation in an elastic layer of uniform thickness. The
layer is subject to an underlying simple shear deformation accompanied by an
arbitrary uniform hydrostatic stress. In respect of a general form of
incompressible,isotropic elastic strain-energy function, the dispersion
equation for infinitesimal waves is obtained asymptotically for incremental
traction boundary conditions on the faces of the layer. Two sets of wavespeeds
as a function of wave number, layer thickness and material parameter are
obtained and the numerical results are illustrated for two different classes of
strain-energy functions. For a particular class of strain energy functions, it
is shown that wave speeds don't depend upon the amount of shear and the
material parameters. For materials not in this special class velocities do
depend upon the shear deformation.
