The equations of incompressible linear viscoelasticity are averaged over the thickness of a thin plate. The basic equations governing the extensional and flexural motion of the plate are obtained when displacements are assumed to be linear across the thickness of the plate. A dispersion relation governing the propagation of flexural waves is obtained which incorporates characterizing parameters of the material. Numerical results are presented for the decay of waves in a semi-infinite plate which is excited harmonically at one boundary. The results show how characterizing parameters affect the decay of waves.