  New exact solutions are exhibited within the framework of finite
viscoelasticity. More precisely, the solutions correspond to finite-amplitude,
transverse, linearly-polarized, inhomogeneous motions superposed upon a finite
homogeneous static deformation. The viscoelastic body is composed of a
Mooney-Rivlin viscoelastic solid, whose constitutive equation consists in the
sum of an elastic part (Mooney-Rivlin hyperelastic model) and a viscous part
(Newtonian viscous fluid model). The analysis shows that the results are
similar to those obtained for the purely elastic case; inter alia, the normals
to the planes of constant phase and to the planes of constant amplitude must be
orthogonal and conjugate with respect to the B-ellipsoid, where B is the left
Cauchy-Green strain tensor associated with the initial large static
deformation. However, when the constitutive equation is specialized either to
the case of a neo-Hookean viscoelastic solid or to the case of a Newtonian
viscous fluid, a greater variety of solutions arises, with no counterpart in
the purely elastic case. These solutions include travelling inhomogeneous
finite-amplitude damped waves and standing damped waves.
